Polytetrahedron
Encyclopedia
Polytetrahedron is a term used for three distinct types of objects, all based
on the tetrahedron
:
on the tetrahedron
Tetrahedron
In geometry, a tetrahedron is a polyhedron composed of four triangular faces, three of which meet at each vertex. A regular tetrahedron is one in which the four triangles are regular, or "equilateral", and is one of the Platonic solids...
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- A uniform convex polychoronUniform polychoronIn geometry, a uniform polychoron is a polychoron or 4-polytope which is vertex-transitive and whose cells are uniform polyhedra....
made up of 600 tetrahedralTetrahedronIn geometry, a tetrahedron is a polyhedron composed of four triangular faces, three of which meet at each vertex. A regular tetrahedron is one in which the four triangles are regular, or "equilateral", and is one of the Platonic solids...
cellCell (geometry)In geometry, a cell is a three-dimensional element that is part of a higher-dimensional object.- In polytopes :A cell is a three-dimensional polyhedron element that is part of the boundary of a higher-dimensional polytope, such as a polychoron or honeycomb For example, a cubic honeycomb is made...
s. It is more commonly known as a 600-cell or hexacosichoron. Other derivative polychora are identified as polytetrahedra, where a qualifying prefix such as rectified or truncated is used. - A connected set of regularRegularThe term regular can mean normal or obeying rules. Regular may refer to:In organizations:* Regular Army for military usage* Regular clergy, members of a religious order subject to a rule of life* Regular Force for usage in the Canadian Forces...
tetrahedra, the 3-dimensional analogue of a polyiamondPolyiamondA polyiamond is a polyform whose base form is an equilateral triangle. The word polyiamond is a back-formation from diamond, because this word is often used to describe the shape of a pair of equilateral triangles placed base to base, and the initial "di-" looked like a Greek prefix meaning...
. Polytetrahedra and polyiamonds are related as polycubePolycubethumb|200px|right|The seven free tetracubesthumb|200px|right|A [[Chirality |chiral]] pentacubethumb|200px|right|Puzzle with a unique solution...
s are related to polyominoPolyominoA polyomino is a plane geometric figure formed by joining one or more equal squares edge to edge. It is a polyform whose cells are squares. It may be regarded as a finite subset of the regular square tiling with a connected interior....
es. Also known as polytets or n-tets. - In origamiOrigamiis the traditional Japanese art of paper folding, which started in the 17th century AD at the latest and was popularized outside Japan in the mid-1900s. It has since then evolved into a modern art form...
, a polypolyhedron is "a compound of multiple linked polyhedralPolyhedronIn elementary geometry a polyhedron is a geometric solid in three dimensions with flat faces and straight edges...
skeletons with uniformEdge-uniformIn geometry, a polytope is isotoxal or edge-transitive if its symmetries act transitively on its edges...
nonintersecting edges" http://www.langorigami.com/science/polypolyhedra/3rd%20OSME%20Polypolyhedra.pdf. There exist two topologically distinct polytetrahedra, each made up of four intersecting triangleTriangleA triangle is one of the basic shapes of geometry: a polygon with three corners or vertices and three sides or edges which are line segments. A triangle with vertices A, B, and C is denoted ....
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