Tetrahedral Stellation of Dodecahedron 1
This model is a sub-symmetric stellation of the
dodecahedron, having only tetrahedral symmetry.
It is quite hard to visualise, but all the faces lie in the same planes as the
faces of a regular dodecahedron. The points may be thought of as 8 of the 20
points of a great stellated dodecahedron.
This is also the shape you get if inscribe a cube in a dodecahedron, cut off
the 6 "tents" to leave just the inscribed cube, then flip the tents over and
extract them from the cube faces instead. My
dodecahedral shape-shifter demonstrates this.