A Collection of Rotating Polyhedra with Icosidodecahedral Symmetry

I’ve received a request to slow down the rotational speed of the polyhedral models I make and post here, and am going to try to do exactly that. First, though, I need to empty my collection of already-made image files which haven’t yet been posted, so that I can start again, with models which rotate more slowly, after deleting all the “speedy” ones. From my backlog of polyhedral images to post, then, here are most of the ones with icosidodecahedral symmetry.

60 hexagons and 30 rhombi

60 rhombi and 120 trapezoids92 faces including 20 enneagons120 of traingle A and 120 of triangle B and 60 rhombi for 300 faces in all

The next one shown has 362 faces — the closest I have come, so far, to a polyhedron with a number of faces which matches the number of days in a year.

362 faces close to a year

big Convex hull

bowtie polyhedron with 20 enneagons and 12 decagons

Convex hhgdull


cool too

irregular pentagons and hexagons

The next one is a variant of the rhombic enneacontahedron, with that polyhedron’s wide rhombic faces replaced by kites, and its narrow rhombi replaced by pairs of isosceles triangles.

kite and triangle variant of the REC

multiple stellated pentagonal dokaiheptacontahedrongif


Stellated Convex hull

Stellated Convex hull 2

Stellated Convex hull 3I call this next one a “thrice-truncated rhombic triacontahedron.”

Thrice-truncated RTCIn the remaining polyhedral images in this post, some faces have been rendered invisible. I do this, on occasion, either so that the front and back of the polyhedra can be seen at the same time, or simply for aesthetic reasons.

CoGSHSnvex hhgdull

Expanded GRID shell

Stellated Convex hull 2b

Stellated Convex hull 3b

All of these images were created using Stella 4d:  Polyhedron Navigator. If you’d like to try this program for yourself, the website to visit for a free trial download is 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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One Response to A Collection of Rotating Polyhedra with Icosidodecahedral Symmetry

  1. Kristi says:

    Stunning. Thanks for the post

    Liked by 1 person

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