Tag Archives: Mathematics

A Symmetrohedron Featuring Regular Heptagons, Regular Hexagons, Irregular Hexagons, and Irregular Pentagon-Pairs

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symmetrohedron featuring heptagons hexagons and pentagons

Symmetrohedra are symmetric polyhedra which have regular polygons for most (but not necessarily all) of their faces. I made this particular one using Stella 4d, which you can try for yourself at this website. Here’s the net for this polyhedron, also.

symmetrohedron featuring heptagons hexagons and pentagons net

This particular symmetrohedron features twelve faces which are regular heptagons, and eight faces which are regular hexagons (shown in yellow). The irregular faces are 24 pentagons, arranged in a dozen pairs, as well as the six green hexagons. That’s 50 faces in all. This solid has pyritohedral symmetry. The most unusual thing about this polyhedron are its 12 heptagonal faces.

A Symmetrohedron Featuring Regular Heptagons and Hexagons, Along with Irregular Quadrilaterals and Triangles

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symmetrohedron

Symmetrohedra are symmetric polyhedra which have regular polygons for most (but not necessarily all) of their faces. I made this particular one using Stella 4d, which you can try for yourself at this website. Here’s the net for this polyhedron, also.

symmetrohedron net

This particular symmetrohedron features 12 faces which are regular heptagons, and 8 faces which are regular hexagons. The irregular faces are 12 isosceles triangles, 24 isosceles trapezoids, and 6 rectangles, for a total of 62 faces. It has pyritohedral symmetry. The most unusual thing about this polyhedron are its 12 heptagonal faces.

A Faceted Truncated Octahedron with Twenty Faces

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Faceted Trunc Octa

The twenty faces of this polyhedron are six small blue squares, six interpenetrating, larger red squares, and eight irregular, interpenetrating yellow hexagons. I made it using Stella 4d: Polyhedron Navigator, which you can try for free at http://www.software3d.com/Stella.php. The squares are easy to find, but it can be a challenge to see the yellow hexagons. In the .gif below, all of the yellow faces but one are hidden, which should make it easier to see where the hexagons are positioned, relative to the squares.

 

Complexes of 101 Great Stellated Dodecahedra Each, Shown with Three Different Coloring Schemes

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GSD complex 101 parts

GSD complex 101 parts parallel faces same color

GSD complex 101 parts rb

I made these .gifs using Stella 4d: Polyhedron Navigator, which you can try for free at http://www.software3d.com/Stella.php.

 

Complexes of 61 Small Stellated Dodecahedra Each, Shown with Three Different Coloring Schemes

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spectral small stellated dodecahedra

spectral small stellated dodecahedra 61

spectral small stellated dodecahedra rb

I made these .gifs using Stella 4d: Polyhedron Navigator, which you can try for free at this website.

A Compound of the Rhombic Triacontahedron and a Truncation of the Icosahedron

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Stellated Dual Morph 50.0%

In the compound above, the yellow hexagons are not quite regular, which is why I’m calling the yellow-and-orange polyhedron a truncation of the icosahedron, rather than simply the truncated icosahedron. I stumbled upon it while playing with Stella 4d, which you may try for free at http://www.software3d.com/Stella.php.