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

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April 30

Identify this polyhedron

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, cmɢʟee⎆τaʟκ 12:38, 30 April 2022 (UTC)

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

References

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)

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)

Thank you very much. Yes, it looks like File:Polyhedron_pair_6-8.png with shorter yellow pyramids. Cheers, cmɢʟee⎆τaʟκ 07:05, 1 May 2022 (UTC)

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)