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Net Stellation facets × 20 A net of a great stellated dodecahedron (surface geometry); twenty isosceles triangular pyramids, arranged like the faces of an icosahedron. It can be constructed as the third of three stellations of the dodecahedron, and referenced as Wenninger model [W22]. Complete net of a great stellated dodecahedron.
3D model of a small stellated dodecahedron. In geometry, the small stellated dodecahedron is a Kepler–Poinsot polyhedron, named by Arthur Cayley, and with Schläfli symbol {5 ⁄ 2,5}. It is one of four nonconvex regular polyhedra. It is composed of 12 pentagrammic faces, with five pentagrams meeting at each vertex.
The rhombicosidodecahedron shares the vertex arrangement with the small stellated truncated dodecahedron, and with the uniform compounds of six or twelve pentagrammic prisms. The Zometool kits for making geodesic domes and other polyhedra use slotted balls as connectors. The balls are "expanded" rhombicosidodecahedra, with the squares replaced ...
Compound of great icosahedron and stellated dodecahedron Type: stellation and compound: Coxeter diagram: ∪ : Convex hull: Dodecahedron: Polyhedra: 1 great icosahedron 1 great stellated dodecahedron: Faces: 20 triangles 12 pentagrams: Edges: 60 Vertices: 32 Symmetry group: icosahedral (I h)
The endo-dodecahedron is concave and equilateral; it can tessellate space with the convex regular dodecahedron. Continuing from there in that direction, we pass through a degenerate case where twelve vertices coincide in the centre, and on to the regular great stellated dodecahedron where all edges and angles are equal again, and the faces have ...
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.
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.
Small stellated dodecahedron; Great dodecahedron; Great stellated dodecahedron This page was last edited on 30 ...