polyhedra | RobertLovesPi.net

Polyhedron Featuring Decagons and Triangles

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Polyhedron Featuring Decagons and Triangles

This was created using Stella 4d, which you may try for free at http://www.software3d.com/stella.php.

Compound of the Rhombic Triacontahedron and a Truncated Icosahedron

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Compound of the Rhombic Triacontahedron and a Truncated Icosahedron

I stumbled across this while manipulating polyhedra with Stella 4d, which you can try for free at http://www.software3d.com/stella.php.

The title describes the blue and yellow figure as “a” truncated icosahedron, rather than “the” truncated icosahedron, because of the slight irregularity of the hexagonal faces, a result of the truncation-planes being slightly closer to the center than is the case for the true Archimedean solid. It should be possible to fix this, but that may be beyond my abilities.

Sixty Irregular Pentagons in a Regular Pattern

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Sixty Irregular Pentagon in a Regular Pattern

Another accidental discovery made while manipulating polyhedra with Stella 4d, which you can try for free at http://www.software3d.com/stella.php.

Polyhedron Featuring Nonagons and Rhombi

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Polyhedron Featuring Nonagons and Rhombi

I stumbled across this while manipulating polyhedra with Stella 4d, which you can try for free at http://www.software3d.com/stella.php.

I don’t think the nonagons are quite regular, and the yellow figures may be near-rhomboidal kites, rather than true rhombi. Nevertheless, I find it an interesting figure, and am posting it here so I can find it for further investigations later.

Icosahedral Shell

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Icosahedral Shell

This was created with Stella 4d, software you can try for free at http://www.software3d.com/stella.php.

A “Bowtie” Variant of the Truncated Icosahedron

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This has the twelve regular pentagons and twenty regular hexagons of a truncated icosahedron (most familiar to the world as the shape upon which most soccer balls are based), but also has pairs of trapezoids in “bowtie” configurations. I discovered this polyhedron using Stella 4d, which you can try for free at http://www.software3d.com/stella.php.

Crescents on a Truncated Octahedron

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Crescents on a Truncated Octahedron

Stella 4d (polyhedral manipulation software) was used to place the image in the previous post on each hexagonal face of a truncated octahedron, and the square faces were hidden. The program can do many other things as well — and you may try it for free at http://www.software3d.com/stella.php.

The Rhombic Enneacontahedron, with Mandalas

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The Rhombic Enneacontahedron, with Mandalas

The rhombic enneacontahedron has ninety faces. In this image, the sixty of them which are wide rhombi are decorated with the mandala, 22, from my last post. The narrow rhombi, of which there are thirty, are colored light blue.

This was created using Stella 4d, which you can try for yourself at http://www.software3d.com/stella.php.