Thirty-Four Rotating, Convex, and Non-Chiral Polyhedra with Icosidodecahedral Symmetry

Most in the field call this type of symmetry “icosahedral,” but I prefer the term George Hart uses — along with “cuboctahedral” in place of “octahedral.”

Each polyhedral image here was created with Stella 4d: Polyhedron Navigator. At this linked page, you can try a trial version of that program for free.

12 icosagons and stuff

Dual of Convex huull

272 faces in 12 reg dec & 120 scalene triangles and 60 isos triangles and 60 isos traps and 20 reg hexagons

Convex hnbghjull

Convex hull 20 8 and 12

By the way, when I described these polyhedra, in this post’s title, as non-chiral, I was not referring to the coloring-schemes used here, many of which obviously are chiral, but only the shapes themselves.

Convex hull LP

convex hull of synthetic comet nucleus

Dual of Convex hull

Convexxx hull

Convhgfehgx hull

That 10 GB space-upgrade, which most bloggers don’t ever need, is really coming in handy right now. In other words, some of these .gif files are huge!

Convhgfex hull

Dual of Chgonvex hulgfl

Dual of Chgonvex hull

Dual of Cjhfjonvex hull

Dualhhc of Convex hull

Why, yes, I am including some words after every fifth polyhedron. That will help, later, when I count them for the title of this post.

Dual of Conjhvex hull

enneagons and kites

Enneagons, Pentagon, isostraps, and rectangles

exansiaon Convex hull

Expanded GRID

I’m not sure why that last one is spinning the opposite direction from the others. Perhaps this polyhedron is trying to start a trend. On the other hand, it could just simply upside-down.

Faceted Stellated Dual of Convex hull

metaexpanded RID

ID variation

intermediate form


That’s twenty-five so far.


pentadecagons two types hexagons and trapezoids

RID variant

RTC and RID blend

Stellated Poly

Clearly, I should have checked the number of files in that file folder before deciding to simply post them all together, based on what they have in common. That’s thirty so far.

sixty pentagons and twenty hexagons

twenty regular dodecagons


what is this thing