Wikipedia:Reference desk/Archives/Mathematics/2022 April 30

Mathematics desk
< April 29 << Mar | April | May >> Current desk >
Welcome to the Wikipedia Mathematics Reference Desk Archives
The page you are currently viewing is a transcluded archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages.


April 30

edit

Identify this polyhedron

edit
 
Shuriken kusudama

Would someone be able to identify the base polyhedron of this origami, which looks like a cross between a "tetrakis hexahedron": http://en.wikipedia.org/wiki/Tetrakis_hexahedron and an "elevated octahedron": http://www.rinusroelofs.nl/projects/elevation-inf/pr-elev-inf-a01.html ? Thanks, cmɢʟeeτaʟκ 12:38, 30 April 2022 (UTC)[reply]

Hi @Cmglee:, this is a variation of Sonobe modular.[1]. I hope this helps. :) Nanosci (talk) 15:58, 30 April 2022 (UTC)[reply]

References

  1. ^ "Shuriken variation". Retrieved 2022-04-30.
As a geometric shape it looks like in might be the union of a regular polyhedron and its dual, as in this image. Hard to make out, though, just from the image, how regular this thing is and what the corresponding symmetries are.  --Lambiam 18:02, 30 April 2022 (UTC)[reply]
I'm inclined to agree with Nanosci, in which case this must be the same as [1], right? (That's a regular octahedron with a pyramid glued to each face, one of whose faces is equilateral and the other three are isosceles right triangles.) --JBL (talk) 20:57, 30 April 2022 (UTC)[reply]
Thank you very much. Yes, it looks like File:Polyhedron_pair_6-8.png with shorter yellow pyramids. Cheers, cmɢʟeeτaʟκ 07:05, 1 May 2022 (UTC)[reply]
I don't think that file is the same thing; the patterned paper here is a red herring as far as the underlying geometry is concerned. By "a regular octahedron with a pyramid glued to each face" I mean what some people call a "stellated" or "augmented" octahedron; the highly decorated corners in the kusudama are the vertices of the octahedron, and the visible purple points are the apexes of the stellating pyramids. --JBL (talk) 18:41, 6 May 2022 (UTC)[reply]