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

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.)

About RobertLovesPi

I go by RobertLovesPi on-line, and am interested in many things, a large portion of which are geometrical. Welcome to my little slice of the Internet. The viewpoints and opinions expressed on this website are my own. They should not be confused with the views of my employer, nor any other organization, nor institution, of any kind.
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