72-Faced Snub Dodecahedron Variant, and Related Polyhedra

72 faced snub dodecahedron variant mirror image

Like the snub dodecahedron itself, which this resembles, this polyhedron is chiral, meaning it exists in left- and right-handed forms. One version is shown above, and its mirror-image is shown below.

72-faced snub dodecahedron variant

With any chiral polyhedron, it is possible to make a compound out of the two mirror-images. Here is the enantiomorphic-pair compound for this polyhedron.

Compound of enantiomorphic pair

After making this compound, I was curious about what sort of convex hull it would have, so I used the program I employ for these polyhedral investigations, Stella 4d (available at http://www.software3d.com/Stella.php), to find out:

Convex hull of compound on enantiomorphic pair

This polyhedron contains irregular icosagons, which are twenty-sided polygons. After playing around with this for a while, I was able to construct a related polyhedron in which the icosagons were regular — and that was one of the polyhedra seen on the post immediately before this one, which I then altered to form the others there. Had I not actually seen it happen myself, I would not have suspected there would be any connection between the snub dodecahedron, and polyhedra containing regular icosagons.

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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