The Truncated Truncated Icosahedron

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The Truncated Truncated Icosahedron

The icosahedron has twenty triangular faces. Truncate it once, and the triangles become hexagons, with pentagons appearing under the pyramids removed in the truncation. This is the “soccer ball” shape familiar to millions.

If you take this figure and truncate it again, the twenty hexagons become twenty dodecagons, the twelve pentagons each become decagons, and sixty isosceles triangles appear under the pyramids removed by this second truncation.

I made this image using Stella 4d, a program you can find at www.software3d.com/Stella.php. Also, just for fun, here’s a version of it with the colors switched around, and with a slight bounce as it rotates in the other direction.

truncated trunctaed icosahedron

A Pentacontahedron Featuring Six Regular Dodecagons, Eight Equilateral Triangles, Twenty-Four Trapezoids, and Twelve Rectangles

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A Pentacontahedron Featuring Six Regular Dodecagons, Eight Equilateral Triangles, Twenty-Four Trapezoids, and Twelve Rectangles

I used Stella 4d, software you can find at http://www.software3d.com/Stella.php, to make this image.