Tag Archives: Mathematics

A Tessellation Featuring Regular Dodecagons, Pentagons, and Triangles, Along With Isosceles Trapezoids and Elongated, Equilateral Octagons

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The Sixth Stellation of the Triakis Octahedron Is a Three-Part Polyhedral Compound

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The components of this compound are eight-faced trapezohedra. Here’s what just one of them looks like:

I made these images using Stella 4d, which you can try for free right here.

Tessellation Featuring Regular Octagons, Regular Pentagons, Squares, Equilateral Hexagons, and Irregular, Convex Pentagons

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18 Octagonal Prisms in a Cuboctahedral Arrangement

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I made this using Stella 4d, which you can try for free right here.

A Near-Miss to a Ring of Twelve Heptagonal Antiprisms

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Twelve heptagonal antiprisms, meeting at triangular faces, can make a ring with only a small gap remaining. It’s a “near miss,” made using Stella 4d, which you can try for free right here.

Tessellation Including Regular Decagons, Hexagons, Pentagons, and Triangles, Along With Several Irregular Polygons

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A Tessellation Featuring Regular Pentagons, Regular Hexagons of Two Sizes, Isosceles Trapezoids, and Equilateral Octagons

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A Tessellation of Regular Hexagons, Regular Heptagons, Convex Pentagons, and Large Areas of Negative Space

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If you don’t want to view part of this as “negative space,” you can instead view the black regions as concave heptaicosagons (27-gons).

A Tessellation of the Plane Using Regular Hexagons and Regular Pentagons, Along With Concave, Equilateral Octagons

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A Polyhedron With 182 Faces and Icosidodecahedral Symmetry

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This polyhedron contains, as faces, 12 regular decagons, 20 regular hexagons, 30 squares, and 120 irregular hexagons. I made it using Stella 4d, which you can try for free at this website.