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3D model of a great stellated dodecahedron. In geometry, the great stellated dodecahedron is a Kepler–Poinsot polyhedron, with Schläfli symbol {5 ⁄ 2,3}. It is one of four nonconvex regular polyhedra. It is composed of 12 intersecting pentagrammic faces, with three pentagrams meeting at each vertex.
Great dodecahemicosacron (Dual of great dodecahemicosahedron) — V(5.6. 5 / 4 .6) π − π / 3 120° Small dodecahemicosacron (Dual of small dodecahemicosahedron) — V( 5 / 2 .6. 5 / 3 .6) π − π / 3 120° Great icosihemidodecacron (Dual of great icosihemidodecacron) — V(3. 10 / 3 . 3 / 2 ...
3D model of a great stellated truncated dodecahedron. In geometry, the great stellated truncated dodecahedron (or quasitruncated great stellated dodecahedron or great stellatruncated dodecahedron) is a nonconvex uniform polyhedron, indexed as U 66. It has 32 faces (20 triangles and 12 decagrams), 90 edges, and 60 vertices. [1]
It can be seen as a polyhedron compound of a great icosahedron and great stellated dodecahedron. It is one of five compounds constructed from a Platonic solid or Kepler-Poinsot solid, and its dual. It is a stellation of the great icosidodecahedron. It has icosahedral symmetry (I h) and it has the same vertex arrangement as a great rhombic ...
Small stellated dodecahedron: Great dodecahedron: 5|2 5 / 2 {5 / 2,5} I h: U34 K39 12 30 12 12{5 / 2} 21 Great dodecahedron: Small stellated dodecahedron: 5 / 2 |2 5 {5, 5 / 2} I h: U35 K40 12 30 12 12{5} 22 Great stellated dodecahedron: Great icosahedron: 3|2 5 / 2 {5 / 2,3} I h: U52 K57 20 30 12 12{5 / 2} 41 Great icosahedron (16th stellation ...
Great triambic icosahedron: Icosahedron: Compound of five cubes: Rhombic triacontahedron: Compound of great icosahedron and great stellated dodecahedron: Icosidodecahedron: Compound of great icosahedron and great stellated dodecahedron: Great icosidodecahedron: Compound of dodecahedron and icosahedron: Icosidodecahedron: Compound of cube and ...
The patterns {m/2, m} and {m, m/2} continue for odd m < 7 as polyhedra: when m = 5, we obtain the small stellated dodecahedron and great dodecahedron, [18] and when m = 3, the case degenerates to a tetrahedron. The other two Kepler–Poinsot polyhedra (the great stellated dodecahedron and great icosahedron) do not have regular hyperbolic tiling ...
The stellation diagram for the regular dodecahedron with the central pentagon highlighted. This diagram represents the dodecahedron face itself. In geometry, a stellation diagram or stellation pattern is a two-dimensional diagram in the plane of some face of a polyhedron, showing lines where other face planes intersect with this one.