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Stellated Truncated Hexahedron

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  • Vertex description: 8/3.8/3.3
  • Faces: 14
  • Edges: 36
  • Vertices: 24
  • External facelets: 54
  • Dual: Great triakisoctahedron
  • Name breakdown:
    • Stellated: Stellate a cube. The cube has no finite stellations, but one can add an infinite stellation cell to each side.
    • Truncated: Truncate the result with planes parallel to the faces of an octahedron.
    • Hexahedron: The cube, a.k.a. hexahedron, we started with.

Also known as the quasitruncated hexahedron, the intersecting faces consist of 6 regular 8/3 octagrams in red, and 8 equilateral triangles in yellow. This polyhedron is a faceting of the rhombicuboctahedron, but not a true stellation of the uniform truncated cube, the core being a nonuniform version. It can also be created by truncating a cube further than usual, back past the other end of each edge, if you can picture that! This is what quasitruncated refers to.

These two nets get you started, and look like the normal nets you would get for this model. I wanted a nice solid model though, so I didn't quite just use the default nets.
Here you see the above parts put together, plus a part that fits at the base. The default nets produced by Great Stella would only have made the small square in the middle. However, before printing out nets, I deselected all the cells of the stellation that comprise the inner cube, leaving the model with holes right through it where those little squares should be.
The only difference this made to the nets produced was that now the whole square base of each part was printed out, with the small square still printed in the middle, intended as a hole to cut out. Instead I glued the whole square base onto each part. The small printed square is convenient for lining up the edges meeting around it (from the yellow part).
The parts are then assembled as a cube would be. This method makes a very rigid model.
The finished model.

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