Polyhedrons

A polyhedron is a three-dimensional object bounded on all sides by polygons and whose edges are shared by exactly two polygons. We look at the various types of polyhedrons found in mathematics.
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[@jimiwills]

Oooh, I live near the national museum of Scotland. Will need to go look for those. They don't always have everything on display though.

[@LaverneMelissaHarding]

The rhombicuboctahedron is usually called a "elongated square orthobicupola" while the pseudorhombicuboctahedron is called the "elongated square gyrobicuopla" Why is that?

[@cheesepufss]

the pseudo-rhombicuboctahedron is a johnson solid, which is one of 92 solids that are convex but not uniform. its better if i explain each pat of the name “elongated square gyrobicupola” separately.
first, a cupola is when you take two polygons, one with twice as many edges as the other, then connect them using an alternating band of squares and triangles. if that doesn’t make sense, just google it. you should get the idea then.
when you take two of those cupolas and join them at their bases, it is a bicupola. however, since cupolae are made up of squares and triangles, it’s possible to have two different orientations. orthobicupolas have their like faces meet, so that squares touch squares and triangles touch triangles. gyrobicupolas have unlike faces meet, so that squares only touch triangles and vice versa.
the square gyrobicupola and orthobicupola are made by doing this to a square cupola, precisely.
elongation is when you insert a prism at the base of a solid, or between the bases if it’s a solid with the prefix “bi.” elongating a square orthobicupola creates the rhombicuboctahedron, and elongating a gyrobicupola creates the pseudo-rhombicuboctahedron.
i hope this helps.