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In the geometry of three dimensions, a stellation extends a polyhedron to form a new figure that is also a polyhedron. The following is a list of stellations of various polyhedra. h The following is a list of stellations of various polyhedra. h
John Conway devised a terminology for stellated polygons, polyhedra and polychora (Coxeter 1974). In this system the process of extending edges to create a new figure is called stellation, that of extending faces is called greatening and that of extending cells is called aggrandizement (this last does not apply to polyhedra). This allows a ...
This is an indexed list of the uniform and stellated polyhedra from the book Polyhedron Models, by Magnus Wenninger. The book was written as a guide book to building polyhedra as physical models. It includes templates of face elements for construction and helpful hints in building, and also brief descriptions on the theory behind these shapes.
The small and great stellated dodecahedra, sometimes called the Kepler polyhedra, were first recognized as regular by Johannes Kepler around 1619. [9] He obtained them by stellating the regular convex dodecahedron, for the first time treating it as a surface rather than a solid. He noticed that by extending the edges or faces of the convex ...
The stellated octahedron is the first iteration of the 3D analogue of a Koch snowflake. A compound of two spherical tetrahedra can be constructed, as illustrated. The two tetrahedra of the compound view of the stellated octahedron are "desmic", meaning that (when interpreted as a line in projective space ) each edge of one tetrahedron crosses ...
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.
Set of concave polyhedra formed either by the same vertices of a convex polyhedra, or by the inclusion of new vertices by intersection of face planes and edges. Wikimedia Commons has media related to Polyhedral stellations .
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 ...