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The gyroelongated triangular bipyramid can be made with equilateral triangles, but is not a deltahedron because it has coplanar faces, i.e. is not strictly convex.
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Convexity is not a defining property of a deltahedron. Would it suffice to drop the "i.e. ..."? —Tamfang (talk) 18:27, 6 January 2011 (UTC)[reply]
Hmmm... MathWorld says they can't be coplanar adjacent faces - assumed since that would allow an unlimited number of solutions as subset surfaces from a partial alternated cubic honeycomb. Tom Ruen (talk) 21:44, 6 January 2011 (UTC)[reply]
Possibly my point was that there are nonconvex solids that are legitimate deltahedra, including stacks of octahedra (hm, is there a height above which it has coplanar – or anti-coplanar – faces?) and the great icosahedron. —Tamfang (talk) 04:44, 8 June 2023 (UTC)[reply]
