Talk:Hexahedron

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Polyhedra Low‑importance

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oh dear this is confusing. what are the actual translations of all the Platonic soldidS? —Preceding unsigned comment added by 70.137.131.117 (talk • contribs) 18:11, 2 April 2007

What do you mean by "actual translations"? —Tamfang 07:37, 15 April 2007 (UTC)[reply]

star hexahedron

pentagrammic pyramid. why didn't you include that? — Preceding unsigned comment added by 99.185.3.0 (talk) 00:31, 23 December 2013 (UTC)[reply]

Looks like there is an unstated restriction to non-intersecting faces here. — Preceding unsigned comment added by 2404:4408:1C43:CD00:0:0:0:2 (talk) 17:41, 8 September 2023 (UTC)[reply]

topo

Is "topologically distinct" the correct term here. They are all homeomorphic to the 3d disk, so topologically, they are all the same. — Preceding unsigned comment added by 129.2.89.87 (talk) 10:57, 27 April 2023 (UTC)[reply]

A partition of a manifold (considering here the surface of the polyhedron) is also a topological concept. —Tamfang (talk)

other cuboids

The categorization of cuboids doesn't have a reference, its not clear what counts as distinct. Except for the last two, they have different symmetry groups. But there are more symmetry groups (or representations) you can get with cuboids:

A "square prism" with two squares and four (congruent) rectangles, symmetry group order 16.
A "rhombic prism" with two rhombi and four rectangles, symmetry group order 8 (but unlike the frustrum has inversion symmetry).
The parallelepiped with two rhombi and four congruent parallelograms, symmetry group order 4. (Mirror plane plus inversion).
Two kites connected by rectangles, again symmetry group order 4.
A skewed variant of the latter (two kites, four parallelograms), symmetry group order 2, but mirror symmetry not inversion symmetry. — Preceding unsigned comment added by 2404:4408:1C43:CD00:0:0:0:2 (talk) 18:04, 8 September 2023 (UTC)[reply]