93 relations: Amsterdam, Antiprism, Archimedean solid, Auschwitz concentration camp, Coxeter–Dynkin diagram, Cross-polytope, Cube, Cuboctahedron, Demihypercube, Dodecahedron, Duoprism, Dutch people, Facet (geometry), Gosset–Elte figures, Haarlem, Harold Scott MacDonald Coxeter, Hypercube, Icosahedron, Icosidodecahedron, Mathematician, Octahedron, Omnitruncated polyhedron, Polytope, Prism (geometry), Quasiregular polyhedron, Rectified 120-cell, Rectified 24-cell, Rectified 5-cell, Rectified 5-cubes, Rectified 5-orthoplexes, Rectified 5-simplexes, Rectified 6-simplexes, Rectified 600-cell, Rectified 7-simplexes, Rectified 8-simplexes, Rectified tesseract, Regular polygon, Rhombicosidodecahedron, Rhombicuboctahedron, Runcinated 24-cells, Runcinated 5-cell, Schläfli symbol, Semiregular polyhedron, Semiregular polytope, Simplex, Sobibór extermination camp, Tesseract, Tetrahedron, Thorold Gosset, Truncated 24-cells, ..., Truncated 5-cell, Truncated cube, Truncated cuboctahedron, Truncated dodecahedron, Truncated icosahedron, Truncated icosidodecahedron, Truncated octahedron, Truncated tetrahedron, Uniform 7-polytope, Uniform 8-polytope, Uniform polytope, 1 22 polytope, 1 32 polytope, 1 42 polytope, 120-cell, 16-cell, 2 21 polytope, 2 31 polytope, 2 41 polytope, 24-cell, 3 21 polytope, 4 21 polytope, 4-polytope, 5-cell, 5-cube, 5-demicube, 5-orthoplex, 5-polytope, 5-simplex, 6-cube, 6-demicube, 6-orthoplex, 6-polytope, 6-simplex, 600-cell, 7-cube, 7-demicube, 7-orthoplex, 7-simplex, 8-cube, 8-demicube, 8-orthoplex, 8-simplex. Expand index (43 more) »

## Amsterdam

Amsterdam is the capital and most populous municipality of the Netherlands.

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## Antiprism

In geometry, an n-sided antiprism is a polyhedron composed of two parallel copies of some particular n-sided polygon, connected by an alternating band of triangles.

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## Archimedean solid

In geometry, an Archimedean solid is one of the 13 solids first enumerated by Archimedes.

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## Auschwitz concentration camp

Auschwitz concentration camp was a network of concentration and extermination camps built and operated by Nazi Germany in occupied Poland during World War II.

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## Coxeter–Dynkin diagram

In geometry, a Coxeter–Dynkin diagram (or Coxeter diagram, Coxeter graph) is a graph with numerically labeled edges (called branches) representing the spatial relations between a collection of mirrors (or reflecting hyperplanes).

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## Cross-polytope

In geometry, a cross-polytope, orthoplex, hyperoctahedron, or cocube is a regular, convex polytope that exists in n-dimensions.

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## Cube

In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex.

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## Cuboctahedron

In geometry, a cuboctahedron is a polyhedron with 8 triangular faces and 6 square faces.

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## Demihypercube

In geometry, demihypercubes (also called n-demicubes, n-hemicubes, and half measure polytopes) are a class of n-polytopes constructed from alternation of an n-hypercube, labeled as hγn for being half of the hypercube family, γn.

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## Dodecahedron

In geometry, a dodecahedron (Greek δωδεκάεδρον, from δώδεκα dōdeka "twelve" + ἕδρα hédra "base", "seat" or "face") is any polyhedron with twelve flat faces.

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## Duoprism

In geometry of 4 dimensions or higher, a duoprism is a polytope resulting from the Cartesian product of two polytopes, each of two dimensions or higher.

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## Dutch people

The Dutch (Dutch), occasionally referred to as Netherlanders—a term that is cognate to the Dutch word for Dutch people, "Nederlanders"—are a Germanic ethnic group native to the Netherlands.

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## Facet (geometry)

In geometry, a facet is a feature of a polyhedron, polytope, or related geometric structure, generally of dimension one less than the structure itself.

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## Gosset–Elte figures

In geometry, the Gosset–Elte figures, named by Coxeter after Thorold Gosset and E. L. Elte, are a group of uniform polytopes which are not regular, generated by a Wythoff construction with mirrors all related by order-2 and order-3 dihedral angles.

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## Haarlem

Haarlem (predecessor of Harlem in the English language) is a city and municipality in the Netherlands.

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## Harold Scott MacDonald Coxeter

Harold Scott MacDonald "Donald" Coxeter, FRS, FRSC, (February 9, 1907 – March 31, 2003) was a British-born Canadian geometer.

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## Hypercube

In geometry, a hypercube is an ''n''-dimensional analogue of a square and a cube.

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## Icosahedron

In geometry, an icosahedron is a polyhedron with 20 faces.

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## Icosidodecahedron

In geometry, an icosidodecahedron is a polyhedron with twenty (icosi) triangular faces and twelve (dodeca) pentagonal faces.

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## Mathematician

A mathematician is someone who uses an extensive knowledge of mathematics in his or her work, typically to solve mathematical problems.

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## Octahedron

In geometry, an octahedron (plural: octahedra) is a polyhedron with eight faces, twelve edges, and six vertices.

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## Omnitruncated polyhedron

In geometry, an omnitruncated polyhedron is a truncated quasiregular polyhedron.

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## Polytope

In elementary geometry, a polytope is a geometric object with "flat" sides.

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## Prism (geometry)

In geometry, a prism is a polyhedron comprising an n-sided polygonal base, a second base which is a translated copy (rigidly moved without rotation) of the first, and n other faces (necessarily all parallelograms) joining corresponding sides of the two bases.

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## Quasiregular polyhedron

In geometry, a quasiregular polyhedron is a semiregular polyhedron that has exactly two kinds of regular faces, which alternate around each vertex.

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## Rectified 120-cell

In geometry, a rectified 120-cell is a uniform 4-polytope formed as the rectification of the regular 120-cell.

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## Rectified 24-cell

In geometry, the rectified 24-cell or rectified icositetrachoron is a uniform 4-dimensional polytope (or uniform 4-polytope), which is bounded by 48 cells: 24 cubes, and 24 cuboctahedra.

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## Rectified 5-cell

In four-dimensional geometry, the rectified 5-cell is a uniform 4-polytope composed of 5 regular tetrahedral and 5 regular octahedral cells.

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## Rectified 5-cubes

In five-dimensional geometry, a rectified 5-cube is a convex uniform 5-polytope, being a rectification of the regular 5-cube.

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## Rectified 5-orthoplexes

In five-dimensional geometry, a rectified 5-orthoplex is a convex uniform 5-polytope, being a rectification of the regular 5-orthoplex.

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## Rectified 5-simplexes

In five-dimensional geometry, a rectified 5-simplex is a convex uniform 5-polytope, being a rectification of the regular 5-simplex.

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## Rectified 6-simplexes

In six-dimensional geometry, a rectified 6-simplex is a convex uniform 6-polytope, being a rectification of the regular 6-simplex.

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## Rectified 600-cell

In geometry, the rectified 600-cell or rectified hexacosichoron is a convex uniform 4-polytope composed of 600 regular octahedra and 120 icosahedra cells.

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## Rectified 7-simplexes

In seven-dimensional geometry, a rectified 7-simplex is a convex uniform 7-polytope, being a rectification of the regular 7-simplex.

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## Rectified 8-simplexes

In eight-dimensional geometry, a rectified 8-simplex is a convex uniform 8-polytope, being a rectification of the regular 8-simplex.

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## Rectified tesseract

In geometry, the rectified tesseract, rectified 8-cell is a uniform 4-polytope (4-dimensional polytope) bounded by 24 cells: 8 cuboctahedra, and 16 tetrahedra.

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## Regular polygon

In Euclidean geometry, a regular polygon is a polygon that is equiangular (all angles are equal in measure) and equilateral (all sides have the same length).

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## Rhombicosidodecahedron

In geometry, the rhombicosidodecahedron, or small rhombicosidodecahedron, is an Archimedean solid, one of thirteen convex isogonal nonprismatic solids constructed of two or more types of regular polygon faces.

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## Rhombicuboctahedron

In geometry, the rhombicuboctahedron, or small rhombicuboctahedron, is an Archimedean solid with eight triangular and eighteen square faces.

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## Runcinated 24-cells

In four-dimensional geometry, a runcinated 24-cell is a convex uniform 4-polytope, being a runcination (a 3rd order truncation) of the regular 24-cell.

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## Runcinated 5-cell

In four-dimensional geometry, a runcinated 5-cell is a convex uniform 4-polytope, being a runcination (a 3rd order truncation, up to face-planing) of the regular 5-cell.

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## Schläfli symbol

In geometry, the Schläfli symbol is a notation of the form that defines regular polytopes and tessellations.

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## Semiregular polyhedron

The term semiregular polyhedron (or semiregular polytope) is used variously by different authors.

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## Semiregular polytope

In geometry, by Thorold Gosset's definition a semiregular polytope is usually taken to be a polytope that is vertex-uniform and has all its facets being regular polytopes.

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## Simplex

In geometry, a simplex (plural: simplexes or simplices) is a generalization of the notion of a triangle or tetrahedron to arbitrary dimensions.

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## Sobibór extermination camp

Sobibór (or Sobibor) was a Nazi German extermination camp built and operated by the SS near the railway station of Sobibór during World War II, within the semi-colonial territory of General Government of the occupied Second Polish Republic.

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## Tesseract

In geometry, the tesseract is the four-dimensional analogue of the cube; the tesseract is to the cube as the cube is to the square.

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## Tetrahedron

In geometry, a tetrahedron (plural: tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges, and four vertex corners.

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## Thorold Gosset

John Herbert de Paz Thorold Gosset (16 October 1869 – December 1962) was an English lawyer and an amateur mathematician.

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## Truncated 24-cells

In geometry, a truncated 24-cell is a uniform 4-polytope (4-dimensional uniform polytope) formed as the truncation of the regular 24-cell.

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## Truncated 5-cell

In geometry, a truncated 5-cell is a uniform 4-polytope (4-dimensional uniform polytope) formed as the truncation of the regular 5-cell.

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## Truncated cube

In geometry, the truncated cube, or truncated hexahedron, is an Archimedean solid.

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## Truncated cuboctahedron

In geometry, the truncated cuboctahedron is an Archimedean solid, named by Kepler as a truncation of a cuboctahedron.

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## Truncated dodecahedron

In geometry, the truncated dodecahedron is an Archimedean solid.

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## Truncated icosahedron

In geometry, the truncated icosahedron is an Archimedean solid, one of 13 convex isogonal nonprismatic solids whose faces are two or more types of regular polygons.

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## Truncated icosidodecahedron

In geometry, the truncated icosidodecahedron is an Archimedean solid, one of thirteen convex isogonal nonprismatic solids constructed by two or more types of regular polygon faces.

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## Truncated octahedron

In geometry, the truncated octahedron is an Archimedean solid.

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## Truncated tetrahedron

In geometry, the truncated tetrahedron is an Archimedean solid.

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## Uniform 7-polytope

In seven-dimensional geometry, a 7-polytope is a polytope contained by 6-polytope facets.

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## Uniform 8-polytope

In eight-dimensional geometry, an eight-dimensional polytope or 8-polytope is a polytope contained by 7-polytope facets.

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## Uniform polytope

A uniform polytope of dimension three or higher is a vertex-transitive polytope bounded by uniform facets.

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## 1 22 polytope

In 6-dimensional geometry, the 122 polytope is a uniform polytope, constructed from the E6 group.

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## 1 32 polytope

In 7-dimensional geometry, 132 is a uniform polytope, constructed from the E7 group.

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## 1 42 polytope

In 8-dimensional geometry, the 142 is a uniform 8-polytope, constructed within the symmetry of the E8 group.

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## 120-cell

In geometry, the 120-cell is the convex regular 4-polytope with Schläfli symbol.

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## 16-cell

In four-dimensional geometry, a 16-cell is a regular convex 4-polytope.

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## 2 21 polytope

In 6-dimensional geometry, the 221 polytope is a uniform 6-polytope, constructed within the symmetry of the E6 group.

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## 2 31 polytope

In 7-dimensional geometry, 231 is a uniform polytope, constructed from the E7 group.

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## 2 41 polytope

In 8-dimensional geometry, the 241 is a uniform 8-polytope, constructed within the symmetry of the E8 group.

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## 24-cell

In geometry, the 24-cell is the convex regular 4-polytope (four-dimensional analogue of a Platonic solid) with Schläfli symbol.

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## 3 21 polytope

In 7-dimensional geometry, the 321 polytope is a uniform 7-polytope, constructed within the symmetry of the E7 group.

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## 4 21 polytope

In 8-dimensional geometry, the 421 is a semiregular uniform 8-polytope, constructed within the symmetry of the E8 group.

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## 4-polytope

In geometry, a 4-polytope (sometimes also called a polychoron, polycell, or polyhedroid) is a four-dimensional polytope.

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## 5-cell

In geometry, the 5-cell is a four-dimensional object bounded by 5 tetrahedral cells.

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## 5-cube

In five-dimensional geometry, a 5-cube is a name for a five-dimensional hypercube with 32 vertices, 80 edges, 80 square faces, 40 cubic cells, and 10 tesseract 4-faces.

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## 5-demicube

In five-dimensional geometry, a demipenteract or 5-demicube is a semiregular 5-polytope, constructed from a 5-hypercube (penteract) with alternated vertices removed.

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## 5-orthoplex

In five-dimensional geometry, a 5-orthoplex, or 5-cross polytope, is a five-dimensional polytope with 10 vertices, 40 edges, 80 triangle faces, 80 tetrahedron cells, 32 5-cell 4-faces.

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## 5-polytope

In five-dimensional geometry, a five-dimensional polytope or 5-polytope is a 5-dimensional polytope, bounded by (4-polytope) facets.

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## 5-simplex

In five-dimensional geometry, a 5-simplex is a self-dual regular 5-polytope.

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## 6-cube

In geometry, a 6-cube is a six-dimensional hypercube with 64 vertices, 192 edges, 240 square faces, 160 cubic cells, 60 tesseract 4-faces, and 12 5-cube 5-faces.

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## 6-demicube

In geometry, a 6-demicube or demihexteract is a uniform 6-polytope, constructed from a 6-cube (hexeract) with alternated vertices removed.

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## 6-orthoplex

In geometry, a 6-orthoplex, or 6-cross polytope, is a regular 6-polytope with 12 vertices, 60 edges, 160 triangle faces, 240 tetrahedron cells, 192 5-cell 4-faces, and 64 5-faces.

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## 6-polytope

In six-dimensional geometry, a six-dimensional polytope or 6-polytope is a polytope, bounded by 5-polytope facets.

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## 6-simplex

In geometry, a 6-simplex is a self-dual regular 6-polytope.

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## 600-cell

In geometry, the 600-cell is the convex regular 4-polytope (four-dimensional analogue of a Platonic solid) with Schläfli symbol.

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## 7-cube

In geometry, a 7-cube is a seven-dimensional hypercube with 128 vertices, 448 edges, 672 square faces, 560 cubic cells, 280 tesseract 4-faces, 84 penteract 5-faces, and 14 hexeract 6-faces.

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## 7-demicube

In geometry, a demihepteract or 7-demicube is a uniform 7-polytope, constructed from the 7-hypercube (hepteract) with alternated vertices removed.

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## 7-orthoplex

In geometry, a 7-orthoplex, or 7-cross polytope, is a regular 7-polytope with 14 vertices, 84 edges, 280 triangle faces, 560 tetrahedron cells, 672 5-cells 4-faces, 448 5-faces, and 128 6-faces.

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## 7-simplex

In 7-dimensional geometry, a 7-simplex is a self-dual regular 7-polytope.

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## 8-cube

In geometry, an 8-cube is an eight-dimensional hypercube (8-cube).

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## 8-demicube

In geometry, a demiocteract or 8-demicube is a uniform 8-polytope, constructed from the 8-hypercube, octeract, with alternated vertices removed.

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## 8-orthoplex

In geometry, an 8-orthoplex or 8-cross polytope is a regular 8-polytope with 16 vertices, 112 edges, 448 triangle faces, 1120 tetrahedron cells, 1792 5-cells 4-faces, 1792 5-faces, 1024 6-faces, and 256 7-faces.

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## 8-simplex

In geometry, an 8-simplex is a self-dual regular 8-polytope.

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## Redirects here:

E L Elte, E. L. Elte, E.L. Elte, EL Elte, Emanuel Elte, Emanuël Elte, Emanuël Lodewijk Elte.

## References

[1] https://en.wikipedia.org/wiki/Emanuel_Lodewijk_Elte