Tag Archives: polyhedron

An Expanded Version of the Rhombic Enneacontahedron

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An Expanded Version of the Rhombic Enneacontahedron

To try the program I use to make these, just visit http://www.software4d.com/stella.php.

Polyhedron Featuring 132 Faces

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Polyhedron Featuring 132 Faces

The 132 faces are:

  • sixty isosceles triangles, in 30 pairs with common bases
  • twelve regular pentagons
  • sixty isosceles triangles with bases on the sides of each pentagon

This polyhedron is the dual of the one in the previous post.

Created using Stella 4d, available at http://www.software3d.com/stella.php.

A Polyhedron with Eighty Faces

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A Polyhedron with 80 Faces

The eighty faces are:

  • twenty hexagons which are equilateral, but not equiangular
  • sixty irregular pentagons

Created using Stella 4d, available at http://www.software3d.com/stella.php.

A Polyhedron with 140 Faces

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Polyhedron with 140 Faces

The 140 faces are:

  • 20 equilateral triangles
  • 60 irregular pentagons
  • 60 non-equilateral, isosceles triangles

Created using Stella 4d, available at http://www.software3d.com/stella.php.

The Eighteenth Stellation of a Rhombicosidodecahedron Which Had Invisible Square Faces

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The Eighteenth Stellation of a Rhombicosidodecahedron Which Had Invisible Square Faces

Created using Stella 4d, software which is available at http://www.software3d.com/stella.php.

Polyhedron Featuring Decagons and Pentagons

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Polyhedron Featuring Decagons and Pentagons

There are twelve regular decagons in this polyhedron, and sixty irregular pentagons. If the pentagons were closer to regularity, this would qualify as a near-miss to the ninety-two Johnson Solids. It is not known how many of these “near-misses” exist — primarily because this group of polyhedra lacks a precise definition.

This polyhedron was discovered with the aid of Stella 4d, software you can try for yourself at http://www.software3d.com/stella.php.

A Ninety-Faced Zonohedron

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A Ninety-Faced Zonohedron

Sixty of the faces of this zonohedron are thombi, and the other thirty are zonogonal octagons.

Software available at http://www.software3d.com/stella.php was used to create this rotating image.

A Polyhedron with 152 Faces

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A Polyhedron with 152 Faces

The faces are:

  • twelve irregular decagons
  • twenty irregular nonagons
  • sixty irregular pentagons
  • sixty isosceles trapezoids

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

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.