Talk:Compound of five octahedra

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Polyhedra Start‑class

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rhombic triacontahedron?

The page says "It can be constructed by a rhombic triacontahedron with rhombic-based pyramids added to all the faces, as shown by the five colored model image", but I don't believe this is true. On casual inspection it appears to be the case, but on more careful examination, the putative bases of those rhombic-based pyramids are seen to be nonplanar. E.g., look at the uppermost blue "pyramid" in the image. The red and green faces which meet its base on the left are clearly coplanar, as are the yellow and orange faces that meet its base on the right. But those green and yellow faces are clearly NOT coplanar. This makes the four points making up the base non-coplanar. Bobhearn (talk) 21:41, 6 February 2010 (UTC)[reply]

Correct. Augmenting each face of the rhombic triacontahedron cannot exactly generate the compound of five octahedra (the resulting 'octahedra' are skewed, with pyritohedral symmetry). However, considering the compound to be a non-self-intersecting solid, it can be smoothly deformed into the augmented rhombic triacontahedron. Hence, it depends whether you are thinking geometrically or topologically. Calcyman (talk) 11:03, 2 June 2010 (UTC)[reply]