Search results
Results From The WOW.Com Content Network
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 ...
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 ...
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 .
In geometry, the first stellation of the rhombic dodecahedron is a self-intersecting polyhedron with 12 faces, each of which is a non-convex hexagon. It is a stellation of the rhombic dodecahedron and has the same outer shell and the same visual appearance as two other shapes: a solid, Escher's solid, with 48 triangular faces, and a polyhedral compound of three flattened octahedra with 24 ...
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.
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.
In Wenninger's book Polyhedron Models, the final stellation of the icosahedron is included as the 17th model of stellated icosahedra with index number W 42. [ 7 ] In 1995, Andrew Hume named it in his Netlib polyhedral database as the echidnahedron after the echidna or spiny anteater, a small mammal that is covered with coarse hair and spines ...