Its
convex hull is the
icosidodecahedron. It also shares its
edge arrangement with the
small dodecahemicosahedron (having the pentagrammic faces in common), and with the
great dodecahemicosahedron (having the pentagonal faces in common). This polyhedron can be considered a
rectified great dodecahedron. It is center of a truncation sequence between a
small stellated dodecahedron and
great dodecahedron: The
truncated small stellated dodecahedron looks like a
dodecahedron on the surface, but it has 24 faces: 12
pentagons from the truncated vertices and 12 overlapping as (truncated pentagrams). The truncation of the dodecadodecahedron itself is not uniform and attempting to make it uniform results in a
degenerate polyhedron (that looks like a
small rhombidodecahedron with {10/2} polygons filling up the dodecahedral set of holes), but it has a uniform quasitruncation, the
truncated dodecadodecahedron. It is topologically equivalent to a
quotient space of the
hyperbolic order-4 pentagonal tiling, by distorting the
pentagrams back into regular
pentagons. As such, it is topologically a
regular polyhedron of index two:
Medial rhombic triacontahedron The
medial rhombic triacontahedron is the
dual of the dodecadodecahedron. It has 30 intersecting
rhombic faces.
Related hyperbolic tiling It is topologically equivalent to a quotient space of the
hyperbolic order-5 square tiling, by distorting the rhombi into
squares. As such, it is topologically a
regular polyhedron of index two: Note that the order-5 square tiling is dual to the
order-4 pentagonal tiling, and a quotient space of the order-4 pentagonal tiling is topologically equivalent to the dual of the medial rhombic triacontahedron, the dodecadodecahedron. == See also ==