Compound of Icosahedron and Dodecahedron

 

compound of icosahedron and dodecahedron

This polyhedron can be made in two colors (as in the picture above) or it can be made in the 5 icosahedron colors + one dodecahedron color.

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To make this figure in only two colors, you can make each vertices pyramid with one folded net.

To see the full-sized template click on this image:       compound of dodecahedron and icosahedron template

You will need to create in two different colors 12 icosahedron vertices (5 equilateral triangles net)(red pyramids in the picture above) and 20 dodecagon vertices (3 isosceles triangle net) (yellow pyramids in the picture above).

For both nets, score the lines that join the triangles. Add tabs along the outside of the template. Bend along the scored lines, and glue. You then have bottomless pyramids with triangular faces. One of your pyramids has a triangular base and the other colored pyramid has a pentagonal base.

To assemble your polyhedron, you should surround every triangle-based pyramid with 3 pentagonal-based pyramids. Every pentagonal-based pyramid should be surrounded by 5 triangle-based pyramids.

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To give the icosahedron of this figure the lovely icosahedral coloring you will need slightly different templates.

To see the full-sized template click on this image:       compound of dodecahedron and icosahedron template

You will need to create 20 dodecahedron vertices (3 isosceles triangle net) in all of the same color. And 60 equilateral triangles for the faces of the icosahedron. You will need 6 triangles of each color. 3 triangles of the same color will surround every dodecahedron vertices.

As in the instructions above, score the lines in the dodecahedron vertices net that join the triangles. Add tabs along the outside of the template. Bend along the scored lines, and glue. You then have a bottomless pyramids with triangular faces and a triangular base. Surround this pyramid with equilateral triangles of the same color.

Repeat this process of surrounding a dodecahedron vertices with 3 triangles of the same color for each of your 5 icosahedron colors. You are now ready to combine these 5 sections to create one-fourth of your polyhedron.

As if you were building a simple icosahedron, combine the large, complex faces of your new icosahedron. Join 5 triangles from your 5 sections to form one icosahedral vertices. You should now be able to join another round of triangles from your sections to create rigid triangular faces of the same color.

As in the icosahedron, place your 6th complex icosahedral face directly across and slightly to the right from the face in your initial grouping of the same color. Add the next 4 complex icosahedral faces in this same way.

Now, by tilting your present creation, consider where the next complex icosahedral face should be placed. That grouping is missing only one color and now you can glue that section into place. Continue in this manner to complete the polyhedron.