A small rhombicuboctahedron is one of the 13 Archimedean solids. It has 26 faces (8 equilateral triangles and 18 squares), 48 edges, and 24 vertices.
To create a small rhombicuboctahedron:
-
Take a cube and cut down each of the 4 edges around the cube, leaving a regular octagonal prism. (Imagine a stack of stop signs.)
- Turn the prism on its side, and make 4 more cuts, just like before.
- Now take the 8 remaining corners, and cut them off, leaving equilateral triangle faces
A layout of the solid looks like this:
+----+
| |
| |
+----+ +----+ +----+ +----+
| | /\ | | /\ | | /\ | | /\
| |/ \| |/ \| |/ \| |/ \
+----+----+----+----+----+----+----+----+
| | | | | | | | |
| | | | | | | | |
+----+----+----+----+----+----+----+----+
| |\ /| |\ /| |\ /| |\ /
| | \/ | | \/ | | \/ | | \/
+----+ +----+ +----+ +----+
| |
| |
+----+
This was one of the shapes that Rubik's Snake could be bent into.
A version of this solid where the bottom layer is rotated 45° is called a pseudorhombicuboctahedron or an elongated square gyrobicupola.
Source:
http://mathworld.wolfram.com/SmallRhombicuboctahedron.html