For the compiler optimization, see Polytope model.
A sculpture of the small stellated dodecahedron in M. C. Escher's Gravitation, near the Mesa+ Institute of Universiteit Twente
A polyhedron model is a physical construction of a polyhedron, constructed from cardboard, plastic board, wood board or other panel material, or, less commonly, solid material.
Since there are 75 uniform polyhedra, including the five regular convex polyhedra, five polyhedral compounds, four Kepler-Poinsot polyhedra, and thirteen Archimedean solids, constructing or collecting polyhedron models has become a common mathematical recreation. Polyhedron models are found in mathematics classrooms much as globes in geography classrooms.
Polyhedron models are notable as three-dimensional proof-of-concepts of geometric theories. Some polyhedra also make great centerpieces, tree toppers, Holiday decorations, or symbols. The Merkaba religious symbol, for example, is a stellated octahedron. Constructing large models offer challenges in engineering structural design.
A polyhedronmodel is a physical construction of a polyhedron, constructed from cardboard, plastic board, wood board or other panel material, or, less...
In geometry, a polyhedron (pl.: polyhedra or polyhedrons; from Greek πολύ (poly-) 'many', and ἕδρον (-hedron) 'base, seat') is a three-dimensional shape...
A geodesic polyhedron is a convex polyhedron made from triangles. They usually have icosahedral symmetry, such that they have 6 triangles at a vertex...
polyhedra from the book PolyhedronModels, by Magnus Wenninger. The book was written as a guide book to building polyhedra as physical models. It includes templates...
In geometry, a uniform polyhedron has regular polygons as faces and is vertex-transitive (i.e., there is an isometry mapping any vertex onto any other)...
In geometry, a toroidal polyhedron is a polyhedron which is also a toroid (a g-holed torus), having a topological genus (g) of 1 or greater. Notable examples...
Platonic solid is a convex, regular polyhedron in three-dimensional Euclidean space. Being a regular polyhedron means that the faces are congruent (identical...
Szilassi polyhedron is a nonconvex polyhedron, topologically a torus, with seven hexagonal faces. The 14 vertices and 21 edges of the Szilassi polyhedron form...
edge set of a triangle, K4 a tetrahedron, etc. The Császár polyhedron, a nonconvex polyhedron with the topology of a torus, has the complete graph K7 as...
stellation is the process of extending a polygon in two dimensions, polyhedron in three dimensions, or, in general, a polytope in n dimensions to form...
In geometry, a pentakis dodecahedron or kisdodecahedron is a polyhedron created by attaching a pentagonal pyramid to each face of a regular dodecahedron;...
the triacontahedron as it is the most common thirty-faced polyhedron, is a convex polyhedron with 30 rhombic faces. It has 60 edges and 32 vertices of...
Encyclopedia of Polyhedra VRML model Conway Notation for Polyhedra Try: "dtO" or "kC" Tetrakis Hexahedron – Interactive Polyhedronmodel The Uniform Polyhedra...
octahedron. It has cubical or octahedral symmetry, and is the only convex polyhedron whose faces are all squares. Its generalization for higher-dimensional...
all regular, the pentagonal prism is a semiregular polyhedron, more generally, a uniform polyhedron, and the third in an infinite set of prisms formed...
In geometry, every polyhedron is associated with a second dual structure, where the vertices of one correspond to the faces of the other, and the edges...
"uniform polyhedra Great icosahedron". Wenninger, Magnus (1974). PolyhedronModels. Cambridge University Press. ISBN 0-521-09859-9. Coxeter, Harold Scott...
Weisstein, Eric W., "Disdyakis dodecahedron" ("Catalan solid") at MathWorld. Disdyakis Dodecahedron (Hexakis Octahedron) Interactive PolyhedronModel...
the book. In Wenninger's book PolyhedronModels, the final stellation of the icosahedron is included as the 17th model of stellated icosahedra with index...
triacontahedron has the most faces of any other strictly convex polyhedron where every face of the polyhedron has the same shape. Projected into a sphere, the edges...
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...
polyhedron to form a new figure that is also a polyhedron. The following is a list of stellations of various polyhedra. List of Wenninger polyhedron models...
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...
In geometry, a uniform polyhedron is a polyhedron which has regular polygons as faces and is vertex-transitive (transitive on its vertices, isogonal, i...
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