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As somebody who has to interpret different types of polyhedra in his research it is sometimes difficult to find a good name for a polyhedron that describes the coordination in a crystal structure. Luckily we can use concepts like capping and distortion to at least give an idea.

Quite recently a co-worker asked me how we would call a polyhedron where the base and opposite site are not the same polygon. So for an octahedron or a trigonal prism we use a triangular base and top and just turn them to either get the octahedron or the trigonal prism.

But what if both sides do not have the same polygon shapes?

So I searched for examples and all I could really find was a polyhedron that was mentioned in J. Lopez et. Al. Comput. Phys. Commun. 2018, 223, 45-54.

Example of a polyhedron with 6 faces and 7 vertices [a]

Source: DOI: 10.1016/j.cpc.2017.09.032

My two questions are, how is the 'category' of polyhedra called where I can find more examples like these? And does this polyhedron have a 'name' or is it characterized by other parameters.

Thank you for all suggestions and ideas, Best Regards

Justanotherchemist
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  • @JeanMarie That's because it is a hexahedron. It has two triangles and four quadrilaterals. This one doesn't seem to have a specific name. – Jaap Scherphuis May 24 '22 at 10:06
  • @Jaap Scherphuis Thank you very much. I should have paid attention to the termination ...hedron $\ne$ gon. – Jean Marie May 24 '22 at 13:18
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    @Jaap Scherphuis I have found here a proposal for a name for this hexahedron: an hemicube or a square hemiprism by reference to the way of obtention (cube truncation). – Jean Marie May 24 '22 at 19:27
  • Hemiprism sounds somewhat interesting. Thank you for that website, I will check it out! So judging by how complicated this is it's no common type of polyhedron either, right? – Justanotherchemist May 25 '22 at 07:10
  • Indeed, non-regular polyhedra are far less studied than regular or semiregular ones. A thought I had: the process described in the reference above is by truncation of an existing polyhedron (a cube). But one could consider your volume as obtained by (also) starting from a cube and gluing two of its neighbor vertices... – Jean Marie May 25 '22 at 07:47

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