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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.
The compound of small stellated dodecahedron and great dodecahedron is a polyhedron compound where the great dodecahedron is internal to its dual, the small stellated dodecahedron. This can be seen as one of the two three-dimensional equivalents of the compound of two pentagrams ({10/4} " decagram "); this series continues into the fourth ...
In 1619 Kepler defined stellation for polygons and polyhedra as the process of extending edges or faces until they meet to form a new polygon or polyhedron.. He stellated the regular dodecahedron to obtain two regular star polyhedra, the small stellated dodecahedron and the great stellated dodecahedron.
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 ...
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 ...
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]
Great dodecahedron {5, 5 / 2 } (5.5.5.5.5) / 2 arccos ( √ 5 / 5 ) 63.435° Great stellated dodecahedron ...
The small and great stellated dodecahedron can be seen as a regular and a great dodecahedron with their edges and faces extended until they intersect. The pentagon faces of these cores are the invisible parts of the star polyhedra's pentagram faces.