96 relations: Alicia Boole Stott, Alternated hypercubic honeycomb, Bitruncation, Cantellated 6-cubes, Cantellated 6-orthoplexes, Cantellated 6-simplexes, Cantellation (geometry), Cantic 6-cube, Cartesian product, Coxeter group, Coxeter–Dynkin diagram, Cross-polytope, Cube, Cyclotruncated 5-simplex honeycomb, Demihypercube, Dimension, Dodecahedron, Dual polyhedron, Duoprism, E6 (mathematics), Expansion (geometry), Face (geometry), Facet (geometry), Factorial, Geometry, Grand antiprism, Greek language, Harold Scott MacDonald Coxeter, Hypercube, Hypercubic honeycomb, Isogonal figure, Ludwig Schläfli, Messenger of Mathematics, Normal (geometry), Norman Johnson (mathematician), Numeral prefix, Omnitruncated 5-simplex honeycomb, Omnitruncation, Pentellated 6-cubes, Pentellated 6-orthoplexes, Pentellated 6-simplexes, Pentic 6-cubes, Permutation, Proprism, Quarter 5-cubic honeycomb, Rectification (geometry), Rectified 6-cubes, Rectified 6-orthoplexes, Rectified 6-simplexes, Regular polygon, ..., Regular polytope, Ring (mathematics), Runcic 6-cubes, Runcinated 6-cubes, Runcinated 6-orthoplexes, Runcinated 6-simplexes, Runcination, Schläfli symbol, Semiregular polytope, Simplex, Six-dimensional space, Steric 6-cubes, Stericated 6-cubes, Stericated 6-orthoplexes, Stericated 6-simplexes, Tesseract, Tetrahedron, Thorold Gosset, Truncated 6-cubes, Truncated 6-orthoplexes, Truncated 6-simplexes, Truncation (geometry), Uniform 4-polytope, Uniform 5-polytope, Uniform k 21 polytope, Uniform polyhedron, Uniform polytope, Vertex figure, Wythoff construction, 1 22 polytope, 120-cell, 16-cell, 2 21 polytope, 24-cell, 5-cell, 5-cube, 5-cubic honeycomb, 5-demicube, 5-demicubic honeycomb, 5-simplex, 5-simplex honeycomb, 6-cube, 6-demicube, 6-orthoplex, 6-polytope, 6-simplex. Expand index (46 more) »

## Alicia Boole Stott

Alicia Boole Stott (8 June 1860 – 17 December 1940) was an Irish-English mathematician.

New!!: Uniform 6-polytope and Alicia Boole Stott · See more »

## Alternated hypercubic honeycomb

In geometry, the alternated hypercube honeycomb (or demicubic honeycomb) is a dimensional infinite series of honeycombs, based on the hypercube honeycomb with an alternation operation.

New!!: Uniform 6-polytope and Alternated hypercubic honeycomb · See more »

## Bitruncation

In geometry, a bitruncation is an operation on regular polytopes.

New!!: Uniform 6-polytope and Bitruncation · See more »

## Cantellated 6-cubes

In six-dimensional geometry, a cantellated 6-cube is a convex uniform 6-polytope, being a cantellation of the regular 6-cube.

New!!: Uniform 6-polytope and Cantellated 6-cubes · See more »

## Cantellated 6-orthoplexes

In six-dimensional geometry, a cantellated 6-orthoplex is a convex uniform 6-polytope, being a cantellation of the regular 6-orthoplex.

New!!: Uniform 6-polytope and Cantellated 6-orthoplexes · See more »

## Cantellated 6-simplexes

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

New!!: Uniform 6-polytope and Cantellated 6-simplexes · See more »

## Cantellation (geometry)

In geometry, a cantellation is an operation in any dimension that bevels a regular polytope at its edges and vertices, creating a new facet in place of each edge and vertex.

New!!: Uniform 6-polytope and Cantellation (geometry) · See more »

## Cantic 6-cube

In six-dimensional geometry, a cantic 6-cube (or a truncated 6-demicube) is a uniform 6-polytope.

New!!: Uniform 6-polytope and Cantic 6-cube · See more »

## Cartesian product

In set theory (and, usually, in other parts of mathematics), a Cartesian product is a mathematical operation that returns a set (or product set or simply product) from multiple sets.

New!!: Uniform 6-polytope and Cartesian product · See more »

## Coxeter group

In mathematics, a Coxeter group, named after H. S. M. Coxeter, is an abstract group that admits a formal description in terms of reflections (or kaleidoscopic mirrors).

New!!: Uniform 6-polytope and Coxeter group · See more »

## 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).

New!!: Uniform 6-polytope and Coxeter–Dynkin diagram · See more »

## Cross-polytope

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

New!!: Uniform 6-polytope and Cross-polytope · See more »

## 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.

New!!: Uniform 6-polytope and Cube · See more »

## Cyclotruncated 5-simplex honeycomb

In five-dimensional Euclidean geometry, the cyclotruncated 5-simplex honeycomb or cyclotruncated hexateric honeycomb is a space-filling tessellation (or honeycomb).

New!!: Uniform 6-polytope and Cyclotruncated 5-simplex honeycomb · See more »

## 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.

New!!: Uniform 6-polytope and Demihypercube · See more »

## Dimension

In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it.

New!!: Uniform 6-polytope and Dimension · See more »

## Dodecahedron

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

New!!: Uniform 6-polytope and Dodecahedron · See more »

## Dual polyhedron

In geometry, any polyhedron is associated with a second dual figure, where the vertices of one correspond to the faces of the other and the edges between pairs of vertices of one correspond to the edges between pairs of faces of the other.

New!!: Uniform 6-polytope and Dual polyhedron · See more »

## 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.

New!!: Uniform 6-polytope and Duoprism · See more »

## E6 (mathematics)

In mathematics, E6 is the name of some closely related Lie groups, linear algebraic groups or their Lie algebras \mathfrak_6, all of which have dimension 78; the same notation E6 is used for the corresponding root lattice, which has rank 6.

New!!: Uniform 6-polytope and E6 (mathematics) · See more »

## Expansion (geometry)

In geometry, expansion is a polytope operation where facets are separated and moved radially apart, and new facets are formed at separated elements (vertices, edges, etc.). Equivalently this operation can be imagined by keeping facets in the same position but reducing their size.

New!!: Uniform 6-polytope and Expansion (geometry) · See more »

## Face (geometry)

In solid geometry, a face is a flat (planar) surface that forms part of the boundary of a solid object; a three-dimensional solid bounded exclusively by flat faces is a polyhedron.

New!!: Uniform 6-polytope and Face (geometry) · See more »

## 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.

New!!: Uniform 6-polytope and Facet (geometry) · See more »

## Factorial

In mathematics, the factorial of a non-negative integer n, denoted by n!, is the product of all positive integers less than or equal to n. For example, The value of 0! is 1, according to the convention for an empty product.

New!!: Uniform 6-polytope and Factorial · See more »

## Geometry

Geometry (from the γεωμετρία; geo- "earth", -metron "measurement") is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space.

New!!: Uniform 6-polytope and Geometry · See more »

## Grand antiprism

In geometry, the grand antiprism or pentagonal double antiprismoid is a uniform 4-polytope (4-dimensional uniform polytope) bounded by 320 cells: 20 pentagonal antiprisms, and 300 tetrahedra.

New!!: Uniform 6-polytope and Grand antiprism · See more »

## Greek language

Greek (Modern Greek: ελληνικά, elliniká, "Greek", ελληνική γλώσσα, ellinikí glóssa, "Greek language") is an independent branch of the Indo-European family of languages, native to Greece and other parts of the Eastern Mediterranean and the Black Sea.

New!!: Uniform 6-polytope and Greek language · See more »

## Harold Scott MacDonald Coxeter

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

New!!: Uniform 6-polytope and Harold Scott MacDonald Coxeter · See more »

## Hypercube

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

New!!: Uniform 6-polytope and Hypercube · See more »

## Hypercubic honeycomb

In geometry, a hypercubic honeycomb is a family of regular honeycombs (tessellations) in n-dimensions with the Schläfli symbols and containing the symmetry of Coxeter group Rn (or B~n-1) for n>.

New!!: Uniform 6-polytope and Hypercubic honeycomb · See more »

## Isogonal figure

In geometry, a polytope (a polygon, polyhedron or tiling, for example) is isogonal or vertex-transitive if all its vertices are equivalent under the symmetries of the figure.

New!!: Uniform 6-polytope and Isogonal figure · See more »

## Ludwig Schläfli

Ludwig Schläfli (15 January 1814 – 20 March 1895) was a Swiss mathematician, specialising in geometry and complex analysis (at the time called function theory) who was one of the key figures in developing the notion of higher-dimensional spaces.

New!!: Uniform 6-polytope and Ludwig Schläfli · See more »

## Messenger of Mathematics

The Messenger of Mathematics is a defunct mathematics journal.

New!!: Uniform 6-polytope and Messenger of Mathematics · See more »

## Normal (geometry)

In geometry, a normal is an object such as a line or vector that is perpendicular to a given object.

New!!: Uniform 6-polytope and Normal (geometry) · See more »

## Norman Johnson (mathematician)

Norman Woodason Johnson (November 12, 1930 – July 13, 2017) was a mathematician, previously at Wheaton College, Norton, Massachusetts.

New!!: Uniform 6-polytope and Norman Johnson (mathematician) · See more »

## Numeral prefix

Numeral or number prefixes are prefixes derived from numerals or occasionally other numbers.

New!!: Uniform 6-polytope and Numeral prefix · See more »

## Omnitruncated 5-simplex honeycomb

In five-dimensional Euclidean geometry, the omnitruncated 5-simplex honeycomb or omnitruncated hexateric honeycomb is a space-filling tessellation (or honeycomb).

New!!: Uniform 6-polytope and Omnitruncated 5-simplex honeycomb · See more »

## Omnitruncation

In geometry, an omnitruncation is an operation applied to a regular polytope (or honeycomb) in a Wythoff construction that creates a maximum number of facets.

New!!: Uniform 6-polytope and Omnitruncation · See more »

## Pentellated 6-cubes

In six-dimensional geometry, a pentellated 6-cube is a convex uniform 6-polytope with 5th order truncations of the regular 6-cube.

New!!: Uniform 6-polytope and Pentellated 6-cubes · See more »

## Pentellated 6-orthoplexes

In six-dimensional geometry, a pentellated 6-orthoplex is a convex uniform 6-polytope with 5th order truncations of the regular 6-orthoplex.

New!!: Uniform 6-polytope and Pentellated 6-orthoplexes · See more »

## Pentellated 6-simplexes

In six-dimensional geometry, a pentellated 6-simplex is a convex uniform 6-polytope with 5th order truncations of the regular 6-simplex.

New!!: Uniform 6-polytope and Pentellated 6-simplexes · See more »

## Pentic 6-cubes

In six-dimensional geometry, a pentic 6-cube is a convex uniform 6-polytope.

New!!: Uniform 6-polytope and Pentic 6-cubes · See more »

## Permutation

In mathematics, the notion of permutation relates to the act of arranging all the members of a set into some sequence or order, or if the set is already ordered, rearranging (reordering) its elements, a process called permuting.

New!!: Uniform 6-polytope and Permutation · See more »

## Proprism

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

New!!: Uniform 6-polytope and Proprism · See more »

## Quarter 5-cubic honeycomb

In five-dimensional Euclidean geometry, the quarter 5-cubic honeycomb is a uniform space-filling tessellation (or honeycomb).

New!!: Uniform 6-polytope and Quarter 5-cubic honeycomb · See more »

## Rectification (geometry)

In Euclidean geometry, rectification or complete-truncation is the process of truncating a polytope by marking the midpoints of all its edges, and cutting off its vertices at those points.

New!!: Uniform 6-polytope and Rectification (geometry) · See more »

## Rectified 6-cubes

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

New!!: Uniform 6-polytope and Rectified 6-cubes · See more »

## Rectified 6-orthoplexes

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

New!!: Uniform 6-polytope and Rectified 6-orthoplexes · See more »

## 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.

New!!: Uniform 6-polytope and Rectified 6-simplexes · See more »

## 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).

New!!: Uniform 6-polytope and Regular polygon · See more »

## Regular polytope

In mathematics, a regular polytope is a polytope whose symmetry group acts transitively on its flags, thus giving it the highest degree of symmetry.

New!!: Uniform 6-polytope and Regular polytope · See more »

## Ring (mathematics)

In mathematics, a ring is one of the fundamental algebraic structures used in abstract algebra.

New!!: Uniform 6-polytope and Ring (mathematics) · See more »

## Runcic 6-cubes

In six-dimensional geometry, a runcic 6-cube is a convex uniform 6-polytope.

New!!: Uniform 6-polytope and Runcic 6-cubes · See more »

## Runcinated 6-cubes

In six-dimensional geometry, a runcinated 6-cube is a convex uniform 6-polytope with 3rd order truncations (runcination) of the regular 6-cube.

New!!: Uniform 6-polytope and Runcinated 6-cubes · See more »

## Runcinated 6-orthoplexes

In six-dimensional geometry, a runcinated 6-orthplex is a convex uniform 6-polytope with 3rd order truncations (runcination) of the regular 6-orthoplex.

New!!: Uniform 6-polytope and Runcinated 6-orthoplexes · See more »

## Runcinated 6-simplexes

In six-dimensional geometry, a runcinated 6-simplex is a convex uniform 6-polytope constructed as a runcination (3rd order truncations) of the regular 6-simplex.

New!!: Uniform 6-polytope and Runcinated 6-simplexes · See more »

## Runcination

In geometry, runcination is an operation that cuts a regular polytope (or honeycomb) simultaneously along the faces, edges and vertices, creating new facets in place of the original face, edge, and vertex centers.

New!!: Uniform 6-polytope and Runcination · See more »

## Schläfli symbol

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

New!!: Uniform 6-polytope and Schläfli symbol · See more »

## 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.

New!!: Uniform 6-polytope and Semiregular polytope · See more »

## Simplex

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

New!!: Uniform 6-polytope and Simplex · See more »

## Six-dimensional space

Six-dimensional space is any space that has six dimensions, six degrees of freedom, and that needs six pieces of data, or coordinates, to specify a location in this space.

New!!: Uniform 6-polytope and Six-dimensional space · See more »

## Steric 6-cubes

In six-dimensional geometry, a steric 6-cube is a convex uniform 6-polytope.

New!!: Uniform 6-polytope and Steric 6-cubes · See more »

## Stericated 6-cubes

In six-dimensional geometry, a stericated 6-cube is a convex uniform 6-polytope, constructed as a sterication (4th order truncation) of the regular 6-cube.

New!!: Uniform 6-polytope and Stericated 6-cubes · See more »

## Stericated 6-orthoplexes

In six-dimensional geometry, a stericated 6-orthoplex is a convex uniform 6-polytope, constructed as a sterication (4th order truncation) of the regular 6-orthoplex.

New!!: Uniform 6-polytope and Stericated 6-orthoplexes · See more »

## Stericated 6-simplexes

In six-dimensional geometry, a stericated 6-simplex is a convex uniform 6-polytope with 4th order truncations (sterication) of the regular 6-simplex.

New!!: Uniform 6-polytope and Stericated 6-simplexes · See more »

## 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.

New!!: Uniform 6-polytope and Tesseract · See more »

## 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.

New!!: Uniform 6-polytope and Tetrahedron · See more »

## Thorold Gosset

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

New!!: Uniform 6-polytope and Thorold Gosset · See more »

## Truncated 6-cubes

In six-dimensional geometry, a truncated 6-cube (or truncated hexeract) is a convex uniform 6-polytope, being a truncation of the regular 6-cube.

New!!: Uniform 6-polytope and Truncated 6-cubes · See more »

## Truncated 6-orthoplexes

In six-dimensional geometry, a truncated 6-orthoplex is a convex uniform 6-polytope, being a truncation of the regular 6-orthoplex.

New!!: Uniform 6-polytope and Truncated 6-orthoplexes · See more »

## Truncated 6-simplexes

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

New!!: Uniform 6-polytope and Truncated 6-simplexes · See more »

## Truncation (geometry)

In geometry, a truncation is an operation in any dimension that cuts polytope vertices, creating a new facet in place of each vertex.

New!!: Uniform 6-polytope and Truncation (geometry) · See more »

## Uniform 4-polytope

In geometry, a uniform 4-polytope (or uniform polychoron) is a 4-polytope which is vertex-transitive and whose cells are uniform polyhedra, and faces are regular polygons.

New!!: Uniform 6-polytope and Uniform 4-polytope · See more »

## Uniform 5-polytope

In geometry, a uniform 5-polytope is a five-dimensional uniform polytope.

New!!: Uniform 6-polytope and Uniform 5-polytope · See more »

## Uniform k 21 polytope

In geometry, a uniform k21 polytope is a polytope in k + 4 dimensions constructed from the ''E''''n'' Coxeter group, and having only regular polytope facets.

New!!: Uniform 6-polytope and Uniform k 21 polytope · See more »

## Uniform polyhedron

A uniform polyhedron is a polyhedron which has regular polygons as faces and is vertex-transitive (transitive on its vertices, isogonal, i.e. there is an isometry mapping any vertex onto any other).

New!!: Uniform 6-polytope and Uniform polyhedron · See more »

## Uniform polytope

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

New!!: Uniform 6-polytope and Uniform polytope · See more »

## Vertex figure

In geometry, a vertex figure, broadly speaking, is the figure exposed when a corner of a polyhedron or polytope is sliced off.

New!!: Uniform 6-polytope and Vertex figure · See more »

## Wythoff construction

In geometry, a Wythoff construction, named after mathematician Willem Abraham Wythoff, is a method for constructing a uniform polyhedron or plane tiling.

New!!: Uniform 6-polytope and Wythoff construction · See more »

## 1 22 polytope

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

New!!: Uniform 6-polytope and 1 22 polytope · See more »

## 120-cell

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

New!!: Uniform 6-polytope and 120-cell · See more »

## 16-cell

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

New!!: Uniform 6-polytope and 16-cell · See more »

## 2 21 polytope

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

New!!: Uniform 6-polytope and 2 21 polytope · See more »

## 24-cell

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

New!!: Uniform 6-polytope and 24-cell · See more »

## 5-cell

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

New!!: Uniform 6-polytope and 5-cell · See more »

## 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.

New!!: Uniform 6-polytope and 5-cube · See more »

## 5-cubic honeycomb

The 5-cubic honeycomb or penteractic honeycomb is the only regular space-filling tessellation (or honeycomb) in Euclidean 5-space.

New!!: Uniform 6-polytope and 5-cubic honeycomb · See more »

## 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.

New!!: Uniform 6-polytope and 5-demicube · See more »

## 5-demicubic honeycomb

The 5-demicube honeycomb, or demipenteractic honeycomb is a uniform space-filling tessellation (or honeycomb) in Euclidean 5-space.

New!!: Uniform 6-polytope and 5-demicubic honeycomb · See more »

## 5-simplex

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

New!!: Uniform 6-polytope and 5-simplex · See more »

## 5-simplex honeycomb

In five-dimensional Euclidean geometry, the 5-simplex honeycomb or hexateric honeycomb is a space-filling tessellation (or honeycomb or pentacomb).

New!!: Uniform 6-polytope and 5-simplex honeycomb · See more »

## 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.

New!!: Uniform 6-polytope and 6-cube · See more »

## 6-demicube

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

New!!: Uniform 6-polytope and 6-demicube · See more »

## 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.

New!!: Uniform 6-polytope and 6-orthoplex · See more »

## 6-polytope

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

New!!: Uniform 6-polytope and 6-polytope · See more »

## 6-simplex

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

New!!: Uniform 6-polytope and 6-simplex · See more »

## Redirects here:

E6-polytope, Pentellation, Uniform 5-honeycomb, Uniform polypeton.

## References

[1] https://en.wikipedia.org/wiki/Uniform_6-polytope