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

jdshfgs

That’s twenty-five so far.

metaRID

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

Unnabsghfmed

what is this thing

About RobertLovesPi

I go by RobertLovesPi on-line, and am interested in many things. The majority of these things 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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2 Responses to Thirty-Four Rotating, Convex, and Non-Chiral Polyhedra with Icosidodecahedral Symmetry

  1. Enrico Bernal says:

    Hi,
    Do you realize that many of your shown polyhedral with non equal edges can have versions with equal edges too? Of course in sense of near misses, the angles of some of the polygons are not regular for those cases.

    I am in contact with a small group of people, from which especially Tadeusz Dorozinsky has posted quite a few of the polyhedrons shown on your website too. Recently sent a few to Robert Webb, and one off them seems to be the same shown in this section (60 Kites or 60 Rhombuses – I’m not sure what you show- go along with 20 non regular hexagons).

    I don’t know if my message might have landed in your spam (due to attachment), but in case you are interested, you can contact

    Bernal.enrico@googlemail.com

    or, if you prefer (since Google always reads with)

    Enrico.bernal@web.de

    Liked by 1 person

    • Yes, and thank you. I often do use the “try to make faces regular” function with Stella 4d. Sometimes I like the “before” and “after” versions, though, and, in that situation, I post both — although not always in the same blog-post.

      Like

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