A Cube-Based “Bowtie” Symmetrohedron Featuring Six Regular Hexadecagons, Eight Equilateral Triangles, and Two Dozen Each of Two Types of Icosceles Trapezoid

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A Cube-Based Symmetrohedron Featuring Six Regular Hexadecagons, Eight Equilateral Triangles, and Two Types of Icosceles Trapezoids

The two types of trapezoid are shown in blue and green. There are twenty-four blue ones (in eights set of three, surrounding each triangle) and twenty-four green ones (in twelve sets of two, with each set in “bowtie” formation).

This symmetrohedron follows logically from one that was already known, and pictured at http://www.cgl.uwaterloo.ca/~csk/projects/symmetrohedra/, with the name “bowtie cube.” Here’s a rotating version of it.

dodecagons and hexagons

(Images created with Stella 4d — software you can try yourself at http://www.software3d.com/Stella.php.)