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Polyhedron Party

Make a constellation of random polyhedra.

Run the code to get a picture of a dodecahedron. Try other polyhedra, like "Octahedron" or "SnubCube":

PolyhedronData["Dodecahedron"]

Choose a polyhedron at random. Rerun the code to get a different polyhedron:

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This gives the complete list of names of polyhedra that are known to the Wolfram Language:

PolyhedronData[]

Choose one polyhedron name at random. Rerun the code to get a different choice:

RandomChoice[PolyhedronData[]]

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RandomChoice[PolyhedronData[]]

Make a picture of a random polyhedron. Rerun the code to get a different polyhedron:

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Wrap the randomly chosen polyhedron name with PolyhedronData to get a picture of it:

PolyhedronData[RandomChoice[PolyhedronData[]]]

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PolyhedronData[RandomChoice[PolyhedronData[]]]

Make a picture of 100 random polyhedra. Rerun the code to get different polyhedra:

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This gives a graphic of a dodecahedron:

PolyhedronData["Dodecahedron"]

You can get the same result by asking for the GraphicsComplex of the dodecahedron and providing a Graphics3D wrapper:

Graphics3D[PolyhedronData["Dodecahedron", "GraphicsComplex"]]

GraphicsComplex gives the vertices and polygons indexed in terms of those vertices for a 3D graphics object:

PolyhedronData["Tetrahedron", "GraphicsComplex"]

The advantage of supplying the Graphics3D wrapper yourself is that you can put more than one polyhedron into the graphic.

This makes a graphic of 100 polyhedra chosen at random. Theyre all positioned in the same place, so they intersect:

Graphics3D[ Table[PolyhedronData[RandomChoice[PolyhedronData[]], "GraphicsComplex"], {100}]]

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Graphics3D[ Table[PolyhedronData[RandomChoice[PolyhedronData[]], "GraphicsComplex"], {100}]]

Move the polyhedra in random directions to spread them out:

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Add a translation to spread out the random polyhedra.

This gives a random number between 0 and 20:

RandomReal[20]

This gives three random numbers:

RandomReal[20, 3]

Put each polyhedron at a random position, using RandomReal to generate a random 3D coordinate:

Graphics3D[ Table[Translate[ PolyhedronData[RandomChoice[PolyhedronData[]], "GraphicsComplex"], RandomReal[20, 3]], {100}]]

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Graphics3D[ Table[Translate[ PolyhedronData[RandomChoice[PolyhedronData[]], "GraphicsComplex"], RandomReal[20, 3]], {100}]]

Add color:

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RandomColor gives a random color. Rerun the code to get a different choice:

RandomColor[]

Give each polyhedron a random color (you need to put the color and the polyhedron in a list, indicated by curly brackets):

Graphics3D[ Table[{RandomColor[], Translate[ PolyhedronData[RandomChoice[PolyhedronData[]], "GraphicsComplex"], RandomReal[20, 3]]}, {100}]]

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Graphics3D[ Table[{RandomColor[], Translate[ PolyhedronData[RandomChoice[PolyhedronData[]], "GraphicsComplex"], RandomReal[20, 3]]}, {100}]]

Share Itmake a website that gives a different polyhedron party each time its visited:

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Deploy the polyhedron party code to the Wolfram Cloud, where anyone with a browser can use it:

CloudDeploy[ Delayed[ExportForm[ Graphics3D[ Table[{RandomColor[], Translate[ PolyhedronData[RandomChoice[PolyhedronData[]], "GraphicsComplex"], RandomReal[20, 3]]}, {100}]], "PNG"]], "Permissions" -> "Public" ]

Click the link in the output to visit the site. Refresh the page in your browser to get a new image.

Tell the world about your creation by sharing the link via email, tweet or other message.

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CloudDeploy[ Delayed[ExportForm[ Graphics3D[ Table[{RandomColor[], Translate[ PolyhedronData[RandomChoice[PolyhedronData[]], "GraphicsComplex"], RandomReal[20, 3]]}, {100}]], "PNG"]], "Permissions" -> "Public" ]