SketchUp

Mathematics, Science, and Technology

1. STANDARD 1
   Analysis, Inquiry, and Design: ENGINEERING DESIGN
   
   Key Idea 1: details
   Engineering design is an iterative process involving modeling and optimization (finding the best solution within given constraints); this process is used to develop technological solutions to problems within given constraints. (Note: The design process could apply to activities from simple investigations to long-term projects.)

   Elementary

   1.1	Describe objects, imaginary or real, that might be modeled or made differently and suggest ways in which the objects can be changed, fixed, or improved
   1.2	Investigate prior solutions and ideas from books, magazines, family, friends, neighbors, and community members
   1.3	Generate ideas for possible solutions, individually and through group activity; apply age-appropriate mathematics and science skills; evaluate the ideas and determine the best solution; and explain reasons for the choices
   1.4	Plan and build, under supervision, a model of the solution using familiar materials, processes, and hand tools
   1.5	Discuss how best to test the solution; perform the test under teacher supervision; record and portray results through numerical and graphic means; discuss orally why things worked or didn't work; and summarize results in writing, suggesting ways to make the solution better

   
   
   

   Intermediate

   T1.1	Identify needs and opportunities for technical solutions from an investigation of situations of general or social interest.
   T1.1a	Identify a scientific or human need that is subject to a technological solution which applies scientific principles	√
   T1.2	Locate and utilize a range of printed, electronic, and human information resources to obtain ideas.	√
   T1.2a	Use all available information systems for a preliminary search that addresses the need.	√
   T1.3	Consider constraints and generate several ideas for alternative solutions, using group and individual ideation techniques (group discussion, brainstorming, forced connections, role play); defer judgment until a number of ideas have been generated; evaluate (critique) ideas; and explain why the chosen solution is optimal.	√
   T1.3a	Generate ideas for alternative solutions	√
   T1.3b	Evaluate alternatives based on the constraints of design	√
   T1.4	Develop plans, including drawings with measurements and details of construction, and construct a model of the solution, exhibiting a degree of craftsmanship.	√
   T1.4a	Design and construct a model of the product or process	√
   T1.4b	Construct a model of the product or process	√
   T1.5	In a group setting, test their solution against design specifications, present and evaluate results, describe how the solution might have been modified for different or better results, and discuss trade-offs that might have to be made.	√
   T1.5a	Test a design	√
   T1.5b	Evaluate a design	√

   
   
   

   Commencement

   1.1	Initiate and carry out a thorough investigation of an unfamiliar situation and identify needs and opportunities for technological invention or innovation
   1.2	identify, locate, and use a wide range of information resources including subject experts, library references, magazines, videotapes, films, electronic data bases and online services, and discuss and document through notes and sketches how findings relate to the problem
   1.3	generate creative solution ideas, break ideas into the significant functional elements, and explore possible refinements; predict possible outcomes using mathematical and functional modeling techniques; choose the optimal solution to the problem, clearly documenting ideas against design criteria and constraints; and explain how human values, economics, ergonomics, and environmental considerations have influenced the solution
   1.4	develop work schedules and plans which include optimal use and cost of materials, processes, time, and expertise; construct a model of the solution, incorporating developmental modifications while working to a high degree of quality (craftsmanship)
   1.5	in a group setting, devise a test of the solution relative to the design criteria and perform the test; record, portray, and logically evaluate performance test results through quanitative, graphic, and verbal means; and use a variety of creative verbal and graphic techniques effectively and persuasively to present conclusions, predict impacts and new problems, and suggest and pursue modifications

   
   
   

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2. STANDARD 2
   INFORMATION SYSTEMS
   
   Key Idea 1: details
   Information technology is used to retrieve, process, and communicate information as a tool to enhance learning.

   Elementary

   1.1	Use computer technology,traditional paper-based resources,and interpersonal discussions to learn, do, and share science in the classroom	√
   1.2	Select appropriate hardware and software that aids in wordprocessing, creating databases, telecommunications, graphing, data display, and other tasks	√
   1.3	Use information technology to link the classroom to world events

   
   
   

   Intermediate

   1.1	Use a range of equipment and software to integrate several forms of information in order to create good-quality audio, video, graphic, and text-based presentations.
   1.2	Use spreadsheets and database software to collect, process, display, and analyze information. Students access needed information from electronic databases and on-line telecommunication services.
   1.3	Systematically obtain accurate and relevant information pertaining to a particular topic from a range of sources, including local and national media, libraries, muse- ums, governmental agencies, industries, and individuals.
   1.4	Collect data from probes to measure events and phenomena.
   1.4a	Collect the data, using the appropriate, available tool
   1.4b	Organize the data
   1.4c	Use the collected data to communicate a scientific concept	√
   1.5	Use simple modeling programs to make predictions.

   
   
   

   Physics

   1.1	Understand and use the more advanced features of word processing, spreadsheets, and database software.
   1.2	Prepare multimedia presentations demonstrating a clear sense of audience and purpose. (Note: Multimedia may include posters, slides, images, presentation software, etc.)	√
   1.2a	Extend knowledge of physical phenomena through independent investigation, e.g., literature review, electronic resources, library research
   1.2b	Use appropriate technology to gather experimental data, develop models,and present results	√
   1.3	Access, select, collate, and analyze information obtained from a wide range of sources such as research databases, foundations, organizations, national libraries, and electronic communication networks, including the Internet.
   1.3a	Use knowledge of physics to evaluate articles in the popular press on contemporary scientific topics
   1.4	Utilize electronic networks to share information.	√
   1.5	Model solutions to a range of problems in mathematics, science, and technology, using computer simulation software.	√
   1.5a	Use software to model and extend classroom and laboratory experiences,recognizing the differences between the model used for understanding and real-world behavior	√

   
   
   

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3. STANDARD 5
   Technology: Engineering Design
   
   Key Idea 1:
   (See Standard 1:ENGINEERING DESIGN)
   
   

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4. STANDARD 5
   Technology: Computer Technology
   
   Key Idea 3: details
   Computers, as tools for design, modeling, information processing, communication, and system control, have greatly increased human productivity and knowledge.

   Elementary

   3.1	Identify and describe the function of the major components of a computer system.
   3.2	Use the computer as a tool for generating and drawing ideas.	√
   3.3	Control computerized devices and systems through programming.	√
   3.4	Model and simulate the design of a complex environment by giving direct commands.	√

   
   
   

   Intermediate

   3.1	Assemble a computer system including keyboard, central processing unit and disc drives, mouse, modem, printer, and monitor
   3.2	Use a computer system to connect to and access needed information from various Internet sites	√
   3.3	Use computer hardware and software to draw and dimension prototypical designs	√
   3.4	Use a computer as a modeling tool	√
   3.5	Use a computer system to monitor and control external events and/or systems	√

   
   
   

   Commencement

   3.1	Understand basic computer architecture and describe the function of computer subsystems and peripheral devices
   3.2	Select a computer system that meets personal needs
   3.3	Attach a modem to a computer system and telephone line, set up and use communications software, connect to various online networks, including the Internet, and access needed information using email, telnet, gopher, ftp, and web searches	√
   3.4	Use computer-aided drawing and design (CADD) software to model realistic solutions to design problems	√
   3.5	Develop an understanding of computer programming and attain some facility in writing computer programs	√

   
   
   

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5. STANDARD 5
   Technology: Technological Systems
   
   Key Idea 4: details
   Technological systems are designed to achieve specific results and produce outputs, such as products, structures, services, energy, or other systems.

   Elementary

   4.1	Identify familiar examples of technological systems that are used to satisfy human needs and wants, and select them on the basis of safety, cost, and function.
   4.2	Assemble and operate simple technological systems, including those with interconnecting mechanisms to achieve different kinds of movement.
   4.3	Understand that larger systems are made up of smaller component subsystems.

   
   
   

   Intermediate

   4.1	Select appropriate technological systems on the basis of safety, function, cost, ease of operation, and quality of post-purchase support
   4.2	Assemble, operate, and explain the operation of simple open- and closed-loop electrical, electronic, mechanical, and pneumatic systems
   4.3	Describe how subsystems and system elements (inputs, processes, outputs) interact within systems
   4.4	Describe how system control requires sensing information, processing it, and making changes	√

   
   
   

   Commencement

   4.1	Explain why making tradeoffs among characteristics, such as safety, function, cost, ease of operation, quality of post-purchase support, and environmental impact, is necessary when selecting systems for specific purposes
   4.2	Model, explain, and analyze the performance of a feedback control system
   4.3	Explain how complex technological systems involve the confluence of numerous other systems

   
   
   

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6. STANDARD 6
   Interconnectedness: Common Themes SYSTEMS THINKING:
   
   Key Idea 1: details
   Through systems thinking, people can recognize the commonalities that exist among all systems and how parts of a system interrelate and combine to perform specific functions.

   Elementary

   1.1	Observe and describe interactions among components of simple systems.	√
   1.2	Identify common things that can be considered to be systems (e.g., a plant population, a subway system, human beings).

   
   
   

   Intermediate

   1.1	Describe the differences between dynamic systems and organizational systems.
   1.2	describe the differences and similarities between engineering systems, natural systems, and social systems.
   1.3	Describe the differences between open- and closed-loop systems.
   1.4	Describe how the output from one part of a system (which can include material, energy, or information) can become the input to other parts.

   
   
   

   Commencement

   1.1	Explain how positive feedback and negative feedback have opposite effects on system outputs.
   1.2	Use an input-process-output-feedback diagram to model and compare the behavior of natural and engineered systems.
   1.3	Define boundary conditions when doing systems analysis to determine what influences a system and how it behaves.

   
   
   

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7. STANDARD 6
   Interconnectedness: Common Themes MODELS:
   
   Key Idea 2: details
   Models are simplified representations of objects, structures, or systems used in analysis, explanation, interpretation, or design.

   Elementary

   2.1	Analyze,construct,and operate models in order to discover attributes of the real thing	√
   2.2	Discover that a model of something is different from the real thing but can be used to study the real thing	√
   2.3	Use different types of models, such as graphs,sketches,diagrams,and maps,to represent various aspects of the real world

   
   
   

   Intermediate

   2.1	Select an appropriate model to begin the search for answers or solutions to a question or problem.
   2.2	Use models to study processes that cannot be studied directly (e.g., when the real process is too slow, too fast, or too dangerous for direct observation).	√
   2.3	Demonstrate the effectiveness of different models to represent the same thing and the same model to represent different things.

   
   
   

   Physics

   2.1	Revise a model to create a more complete or improved representation of the system.
   2.2	Collect information about the behavior of a system and use modeling tools to represent the operation of the system.	√
   2.2a	Use observations of the behavior of a system to develop a model
   2.3	Find and use mathematical models that behave in the same manner as the processes under investigation.
   2.3a	Represent the behavior of real-world systems,using physical and mathematical models	√
   2.4	Compare predictions to actual observations, using test models.	√
   2.4a	Validate or reject a model based on collated experimental data	√
   2.4b	Predict the behavior of a system,using a model	√

   
   
   

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8. STANDARD 7
   Interdisciplinary Problem Solving STRATEGIES:
   
   Key Idea 2: details
   Solving interdisciplinary problems involves a variety of skills and strategies, including effective work habits; gathering and processing information; generating and analyzing ideas; realizing ideas; making connections among the common themes of mathematics, science, and technology; and presenting results.

   Physics

   2.1	Collect,analyze,interpret,and present data,using appropriate tools	√
   2.2	When students participate in an extended,culminating mathematics,science,and technology project, then students should:
   	Work effectively—Contributing to the work of a brainstorming group, laboratory partnership, cooperative learning group, or project team; planning procedures; identify and managing responsibilities of team members; and staying on task, whether working alone or as part of a group.	√
   	Gather and process information —Accessing information from printed media, electronic data bases, and community resources and using the information to develop a definition of the problem and to research possible solutions.	√
   	Generate and analyze ideas — Developing ideas for proposed solutions, investigating ideas, collecting data, and showing relationships and patterns in the data.	√
   	Observe common themes—Observing examples of common unifying themes, applying them to the problem, and using them to better understand the dimensions of the problem.	√
   	Realize ideas—Constructing components or models, arriving at a solution, and evaluating the result.	√
   	Present results—Using a variety of media to present the solution and to communicate the results.	√

   
   
   

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CDOS

• Standard 2: Integrated Learning

  details
  Students will demonstrate how academic knowledge and skills are applied in the workplace and other settings.
  
  Integrated learning encourages students to use essential academic concepts, facts, and procedures in applications related to life skills and the world of work. This approach allows students to see the usefulness of the concepts that they are being asked to learn and to understand their potential application in the world of work.
  
  

  Elementary

  2.1	Identify academic knowledge and skills that are required in specific occupations
  2.2	Demonstrate the difference between the knowledge of a skill and the ability to use the skill	√
  2.3	Solve problems that call for applying academic knowledge and skills.	√

  
  
  

  Intermediate

  2.1	Apply academic knowledge and skills using an interdisciplinary approach to demonstrate the relevance of how these skills are applied in work-related situations in local, state, national, and international communities
  2.2	Solve problems that call for applying academic knowledge and skills	√
  2.3	Use academic knowledge and skills in an occupational context, and demonstrate the application of these skills by using a variety of communication techniques (e.g., sign language, pictures, videos, reports, and technology).

  
  
  

  Commencement

  2.1	Demonstrate the integration and application of academic and occupational skills in their school learning, work, and personal lives.
  2.2	Use academic knowledge and skills in an occupational context, and demonstrate the application of these skills by using a variety of communication techniques (e.g., sign language, pictures, videos, reports, and technology)
  2.3	Research, interpret, analyze, and evaluate information and experiences as related to academic knowledge and technical skills when completing a career plan.

  
  
  

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• Standard 3a: Universal Foundation Skills

  details
  Students will demonstrate mastery of the foundation skills and competencies essential for success in the workplace.
  
  

  1. Thinking skills

     Thinking skills lead to problem solving, experimenting, and focused observation and allow the application of knowledge to new and unfamiliar situations.
     
     

     Elementary

     3.2.1

     Use ideas and information to make decisions and solve problems related to accomplishing a task.

     √

     
     
     

     Intermediate

     3.2.1

     Evaluate facts, solve advanced problems, and make decisions by applying logic and reasoning skills.

     √

     
     
     

     Commencement

     3.2.1

     Demonstrate the ability to organize and process information and apply skills in new ways.

     √

     
     
     
  2. Technology
     Technology is the process and product of human skill and ingenuity in designing and creating things from available resources to satisfy personal and societal needs and wants.
     
     

     Elementary

     3.5.1

     Demonstrate an awareness of the different types of technology available to them and of how technology affects society.

     
     
     

     Intermediate

     3.5.1

     Select and use appropriate technology to complete a task.

     √

     
     
     

     Commencement

     3.5.1

     Apply their knowledge of technology to identify and solve problems.

     √

     
     
     
     
     
  3. Managing Resources
     Using resources includes the application of financial and human factors, and the elements of time and materials to successfully carry out a planned activity.

     Elementary

     3.7.1

     Demonstrate an awareness of the knowledge, skills, abilities, and resources needed to complete a task.

     √

     
     
     

     Intermediate

     3.7.1

     Understand the material, human, and financial resources needed to accomplish tasks and activities.

     √

     
     
     

     Commencement

     3.7.1

     Allocate resources to complete a task.

     √

     
     
     
     
     
  4. Systems
     Systems skills include the understanding of and ability to work within natural and constructed systems.

     Elementary

     3.8.1

     Demonstrate understanding of how a system operates and identify where to obtain information and resources within the system.

     √

     
     
     

     Intermediate

     3.8.1

     Understand the process of evaluating and modifying systems within an organization.

     √

     
     
     

     Commencement

     3.8.1

     Demonstrate an understanding of how systems performance relates to the goals, resources, and functions of an organization.

     √

     
     
     
  
  
  

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• Standard 3b: Career Majors

  details
  Students who choose a career major will acquire the career-specific technical knowledge/skills necessary to progress toward gainful employment, career advancement, and success in postsecondary programs.
  
  
  • Engineering/Technologies
    
    

    Core, Specialized and Experiential

    3b.1	Foundation Development—Develop practical understanding of engineering technology through reading, writing, sample problem solving, and employment experiences.
    3b.2	Technology—Demonstrate how all types of engineering/technical organizations, equipment (hardware/software), and well-trained human resources assist and expedite the production/distribution of goods and services
    3b.3	Engineering/Industrial Processes—Demonstrate knowledge of planning, product development and utilization, and evaluation that meets the needs of industry.

    
    
    
  
  
  

Selection Tool

Use this tool when you want to select part of your project - a line, a wall, a box, etc. If you select a line or wall with this tool then you can hit delete on your keyboard to erase your selection.

This tool is not for moving things around! Use the move/copy tool if you need to move things around.

3D

Use this tool to create 3D text. Click on the tool, fill in the options in the box that pops up, and then click on your project where you want to place the text.

Arc

You use this tool to draw arcs (curves). Click where you want to start the arc, then click where you want to end the arc. Move your mouse around to adjust to curve, and when you have it the way you want it, click again to complete the arc.

Axes

Use this tool to reposition the location of your axes.

Circle

You use the circle tool to draw flat circles!

Component Maker

Dimensional>

The dimension tool can be used to measure the length and width of a shape.

Eraser

The eraser tool will remove lines from your project. Click on lines to remove them from your shapes.

Note that removing lines will sometimes remove walls! If you remove a bounding line for a wall, the wall will disappear.

Follow Me

This tool is useful for making spheres, donuts and other irregular tunnel-shapes. Draw a curve, and then draw the shape you want to follow your curve. With the follow me tool, click and drag your shape along the curve.

Freehand

Use this tool to draw irregular shapes for your project. Also handy when used with the follow me tool.

Line

Use this tool to draw a straight line anywhere in your project. Very helpful for dividing things like walls, or putting things into your project like doors.

Look Around

Use this tool to "look around" in your project. Clicking and dragging with this tool create the equivalent effect of standing in place and looking up, down, left, right, etc.

Move/Copy

Use this tool to move things around or to copy things.

Offset

Use this tool to make duplicates of flat surfaces you have already created, just in a different scale (this is very helpful when creating walls).

To use this tool, click and drag on the surface of your shapes to create a similar shape on the surface of your existing object.

Orbit

Use this tool to adjust the view of your project by rotating your position. Click and drag on your project to use this tool.

Paint Bucket

Use this tool to choose colors and to add color/texture to your walls and shapes. Click on this tool to bring up the colors palette. Choose a color, and then click on your objects to add the color or texture to your objects.

Pan

This tool will change your view of your world by moving you to the up/down/left/right, according to the direction you drag. Unlike the orbit tool, the pan tool will not rotate your view. Click and drag across your project to use this tool.

Polygon

Use this tool to draw polygons other than squares and rectangles (such as octagons, triangles, etc).

Position Camera

Use this tool to reposition your camera. Click anywhere on your project, and the camera (your point of view) will move to that position.

Previous View

Use this tool to go back to your previous view. For example, if you accidentally change your view, click this tool to go back to the view you just had.

Protractor

This tool measures angles - use it to plan the creation of angles, or to measure angles you've already created.

Push/Pull

Use this tool to give your shapes volume (ie, once you have a shape like a rectangle, use this tool to pull up on it to make a cube).

Rectangle

Use this tool to draw a flat rectangle.

Rotate

The rotate tool rotates objects, walls, and components. It works best on FLAT surfaces!

To use the rotate tool, click on a (preferably) flat surface to select the object you want to rotate. Move your mouse away from where you just clicked and click again. To start the rotation, move your mouse around. When your object is properly rotated, click to stop the rotation.

Scale

Use this tool to change the size of one of your objects. Click on the object you want to scale, and drag on the corners to change its size. Hold down your shift key to keep it in proportion.

Section

Tape measure

Use this tool to measure how long something is in sketchup. Click at your starting point, and click again at your ending point. The measurement will show up in the bottom right hand corner of the window.

Text

This tool creates little signs that are attached to your buildings and objects. Use it to display information about your project.

With the tool selected, click on an object and then type the text you want to be displayed.

Walk

Using this tool can create the perspective of walking. Click and hold down on your mouse to start using this tool. Keep your mouse held down and move your cursor left and right - it should look like you are turning. Move your mouse up and down to move forwards and backwards.

Zoom Extents

Use this tool to display your entire project. If you are ever zoomed in too far or need to reset your view, click on this tool to reposition your entire project.

Zoom Window

Another type of zooming tool.

Zoom

This tool zooms your view in and out. Click it once to zoom in a little bit, or click and drag over an area you want to zoom in on.

Note that you can also zoom in (and out!) by using the scroll wheel on your mouse of you have one.

The Fibonacci Series and the Golden Rectangle

1. Select Window>Model Info
   
   
   

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2. Change the format to Decimal and Millimeters:
   
   
   

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3. Change to Top View
   
   
   

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4. Select the Rectangle Tool. Drag the rectangle tool from the origin out until you see the diagonal line and the words Golden Section pop up
   
   
   

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5. To find out the dimensions, CTRL+click on a segment and choose entity info
   
   
   
   
   

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6. Do the same for the other segment:
   
   
   

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7. Use a calculator to determine the ratio.
   1170.6/1894.1=.61802439153
   
   

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8. Drag the rectangle tool to draw a square within the rectangle:
   
   
   

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9. If you keep dividing, you'll end up with a spiral
   
   
   

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The Fibonacci Series and the Golden Rectangle

The original problem that Fibonacci investigated (in the year 1202) was about how fast rabbits could breed in ideal circumstances.

Suppose a newly-born pair of rabbits, one male, one female, are put in a field. Rabbits are able to mate at the age of one month so that at the end of its second month a female can produce another pair of rabbits. Suppose that the rabbits never die and that the female always produces one new pair (one male, one female) every month from the second month on. The puzzle that Fibonacci posed was...

How many pairs will there be in one year?

• At the end of the first month, they mate, but there is still one only 1 pair.
• At the end of the second month the female produces a new pair, so now there are 2 pairs of rabbits in the field.
• At the end of the third month, the original female produces a second pair, making 3 pairs in all in the field.
• At the end of the fourth month, the original female has produced yet another new pair, the female born two months ago produces her first pair also, making 5 pairs.

The number of pairs of rabbits in the field at the start of each month is 1, 1, 2, 3, 5, 8, 13, 21, 34, ...

The golden ratio is obtained by taking the ratio of successive terms in the Fibonacci series:

• 2/1 = 2
• 3/2 = 1.5
• 5/3 = 1.6666...
• 8/5 = 1.6
• 13/8 = 1.625
• 21/13 = 1.61538...
• 34/21 = 1.61904...

and so on, with each addition coming ever closer to multiplying by some as-yet-undetermined number. The number that this ratio is oscillating around is phi (1.6180339887499...).

if you start with two small squares of size 1 next to each other. On top of both of these draw a square of size 2 (=1+1). You can now draw a new square - touching both a unit square and the latest square of side 2 - so having sides 3 units long; and then another touching both the 2-square and the 3-square (which has sides of 5 units). You can continue adding squares around the picture, each new square having a side which is as long as the sum of the latest two square's sides . This set of rectangles whose sides are two successive Fibonacci numbers in length and which are composed of squares with sides which are Fibonacci numbers, or Fibonacci Rectangles.

function fibonacci(theNumber) {
   	var Phi= (1+ Math.sqrt(5))/2; // The Golden section constant
	return (Math.round((Math.pow(Phi, i)/Math.sqrt(5))));
}

Basic Cube

1. Open a new document
   
   

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2. Select the eraser and click on the figure to delete her.
   
   

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3. Select the rectangle tool
   
   
   

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4. Start at the origin and pull outward. As long as you see the diagonal, you will have a square:
   
   
   

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5. Orbit the drawing
   
   
   

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6. Press Space bar and select the edge:
   
   
   

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7. Select the Rotate tool and click on the endpoint-this is where you'll rotate from. The protractor should be green
   
   
   

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8. Click at 90°:
   
   
   

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9. Press Option to make a copy and drag so that your copied line aligns with the Blue axis. You should see that the angle equals 90° in the box in the lower right hand corner:
   
   
   
   

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10. Repeat the process for the other corner:
    
    
    

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11. Select the Orbit tool and move around so that you can see your square as well as your two lines:
    
    
    

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12. Select the Push/Pull Tool and pull the square to meet the two lines:
    
    
    

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Truncated Cube

1. Begin with a cube
   
   

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2. CTRL+click on the right line and select divide:
   
   
   

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3. Move the mouse to make three segments
   
   
   

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4. Divide the top line into three segments
   
   
   

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5. Divide the bottom line into three segments
   
   

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6. Divide the last line, then connect the endpoints:
   
   
   

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7. Continue dividing and connecting:
   
   
   

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8. Delete the corner pyramids and color the faces:
   
   
   

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cuboctahedron Approach 1

1. Begin with a cube
   
   

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2. Select the line tool and bisect a plane:
   
   
   

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3. Connect the midpoints on the face:
   
   
   

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4. Select the eraser tool and delete the vertical and horizontal line segments
   
   
   

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5. Connect the midpoints on every face:
   
   
   

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6. Delete the corner pyramids
   
   
   

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7. Color the planes
   
   
   

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8. If you SHIFT+click on a plane with a color selected, all the planes of the same color will fill with the new color:
   
   
   

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cuboctahedron Approach 2

1. Create a basic Cube
   
   

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2. Connect the near left corner to the far right corner of the top face
   
   
   

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3. Enable X-ray view by selecting View>Face Style>X-Ray
   
   

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4. Connect the far left corner to the near right corner of the bottom face
   
   
   

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5. Delete all the edges of the cube
   
   

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6. Connect the vertices:
   
   

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7. Turn off X-ray
   
   
   

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1. Select the Polygon tool
   And type the number 3. It will show up in the lower right hand corner. Press RETURN
   
   
   

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2. Change the view to top by selecting Camera>Standard Views>Top
   
   
   

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3. Draw a triangle so that one of the vertices falls along the green axis. Start at the origin and drag up along the green axis:
   
   
   

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4. Select the triangle, CTRL+click and choose explode Curve. This process separates the edges from the faces:
   
   
   

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5. Bisect the triangle
   
   
   

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6. Bisect the triangle again:
   
   
   

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7. Orbit the triangle, Select the segment connecting the last two points along the green axis. Choose the Rotate tool. Move the cursor until the protractor is red. Move the protractor to the top of the screen, when it is red, hold down SHIFT and move it to the endpoint. While still holding SHIFT rotate the protractor until the dotted blue line appears
   
   
   
   
   

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8. Press OPTION and rotate the protractor again to rotate the segment along the blue axis:
   
   
   

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9. Connect the vertical line to the intersecting point:
   
   
   

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10. Rotate the hypotenuse of this triangle up vertically. Use the protractor, if you need to adjust the angle type 45:
    
    
    

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11. Delete the hypotenuse and adjacent edge:
    
    
    

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12. Connect two corners to the top of the rotated line:
    
    

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13. Delete the rotated line and connect the last vertex to the top:
    
    

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14. By connecting the midpoints to the vertices, you end up with more tetrahedrons:
    
    
    

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Truncated Tetrahedron

1. Start out with a tetrahedron
   
   
   

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2. CTRL+click on each edge and divide into 3:
   
   
   

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3. Connect the vertices
   
   
   

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4. Delete the pyramids
   
   
   

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Basic Octahedron

1. Start with a Stellated Octahedron
   
   1. Begin with a cube
      
      

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   2. Use the line tool to connect corner to corner:
      
      
      

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   3. Connect all corners:
      
      
      
      

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   4. Delete all the edges of the original cube:
      
      
      

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2. Color the faces (you should have 8 colors)
   
   
   

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3. Select the entire model, press space bar and click on an edge. Select Intersect Faces>with Selection:
   
   

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4. Delete the 8 pyramids:
   
   
   

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Stellated Octahedron

1. Begin with a cube
   
   

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2. Use the line tool to connect corner to corner:
   
   
   

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3. Connect all corners:
   
   
   
   

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4. Delete all the edges of the original cube:
   
   
   

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Truncated Octahedron

1. Begin with an octahedron
   
   
   

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2. Press the spacebar and CTRL click on a line. Select Divide
   
   
   

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3. Divide each line segment into thirds, then use the Line tool to connect all the endpoints
   
   
   
   

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4. Divide all the segments and connect all the endpoints the
   
   
   

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5. Delete the pyramids
   
   
   

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6. This is known as a truncated octahedron:
   
   
   

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Starting with a Stellated Octahedron

1. Start with a Stellated Octahedron
   
   1. Begin with a cube
      
      

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   2. Use the line tool to connect corner to corner:
      
      
      

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   3. Connect all corners:
      
      
      
      

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   4. Delete all the edges of the original cube:
      
      
      

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2. Color the faces (you should have 8 colors)
   
   
   

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3. Select the entire model, press space bar and click on an edge. Select Intersect Faces>with Selection:
   
   

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4. Delete the 8 pyramids:
   
   
   

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5. Ctrl+click on a line and select Divide:
   
   Divide each segment into thirds.
   
   
   

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6. Using the line tool, divide the face like this:
   
   
   

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7. Continue dividing all the faces:
   
   
   
   

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8. Erase the pyramids and extra edges that are left because of dividing the lines into thirds:
   
   
   

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9. Using the line tool, connect the midpoints
   
   
   

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10. Continue connecting midpoints until you have the icosahedron
    
    
    

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Starting with a Golden Rectangle

1. Start with a Golden Rectangle of any length
   
   

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2. Select the rectangle, then CTRL+click on it and select Make Group
   
   
   

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3. Select the move tool . Click on the midpoint at the top of the rectangle and slide left to the origin
   
   
   

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4. With the move tool still selected, click on the midpoint on the left segment and drag up to the axis aligned with the origin
   
   
   

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5. Click in the center and click again, the rectangle should stay put.
   
   

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6. Select the Rotate tool and click at the origin. Press either CTRL or Option to make a copy, then click anywhere for the first rotation, but then move the cursor until the copied rectangle is vertical (rotated 90°):
   
   
   

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7. Select the Orbit tool and orbit the object until you get a view similar to this:
   
   
   

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8. Select the new rectangle and then select the Rotate tool again. Move the cursor up until the protractor is green. Press SHIFT to lock the protractor in its orientation, then click on the origin:
   
   
   

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9. Rotate the selection (you are not making a copy)
   
   
   

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10. Obit and select the Rotate tool. Move the Cursor until you get a red protractor
    
    
    

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11. Rotate a copy of the second rectangle 90°
    
    
    

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12. With the new rectangle still selected, place the protractor flat on the origin and rotate 90°
    You should have 3 intersecting Golden Rectangles:
    
    
    

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13. Select the entire model and CTRL+ click. Select Explode (this will ungroup the rectangles)
    
    
    

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14. Using the Line tool connect the endpoints to create triangles
    
    
    
    
    
    
    
    
    
    
    
    
    

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15. Extra: Now delete the triangles:
    
    
    

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