Talk:Hexahedron

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"? &mdash;Tamfang 07:37, 15 April 2007 (UTC)

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)


 * 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)

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)


 * 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)