Talk:Isotoxal polytope

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Pseudo-isotoxals[edit source]

Is there a polyhedron where the two faces are congruent for each edge and meet in the same way at the same dihedral angle, but is not isotoxal? That is, given any two edges, there is an isometry that transforms one edge and its adjacent faces to match the other, but for at least one edge no such isometries are symmetries. Vel (talk) 18:07, 23 May 2023 (UTC)

A sort of + polycube, made as a blend of 7 cubes might meet this description. Each edge has 2 squares meeting at 90 degrees. It thus meets the formal statement in terms of isometries, however some of the edges are concave while the others are convex, which might have not been what you were looking for. Sycamore918 (talk) 12:58, 24 May 2023 (UTC)