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geometry, there are 127 uniform polytopes with E7 symmetry. The three simplest forms are the 321, 231, and 132 polytopes, composed of 56, 126, and 576 vertices
E7_polytope
Seven-dimensional geometric object
7-polytope is a polytope contained by 6-polytope facets. Each 5-polytope ridge being shared by exactly two 6-polytope facets. A uniform 7-polytope is
Uniform_7-polytope
Geometric object with flat sides
In elementary geometry, a polytope is a geometric object with flat sides (faces). Polytopes are the generalization of three-dimensional polyhedra to any
Polytope
Uniform Polytope
In 7-dimensional geometry, 231 is a uniform polytope, constructed from the E7 group. Its Coxeter symbol is 231, describing its bifurcating Coxeter-Dynkin
2_31_polytope
Polytope in 8-dimensional geometry
In 8-dimensional geometry, the 421 is a semiregular uniform 8-polytope, constructed within the symmetry of the E8 group. It was discovered by Thorold Gosset
4_21_polytope
Uniform polytope
In 7-dimensional geometry, 132 is a uniform polytope, constructed from the E7 group. Its Coxeter symbol is 132, describing its bifurcating Coxeter-Dynkin
1_32_polytope
Uniform polytope in 8 dimensional geometry
In 8-dimensional geometry, the 241 is a uniform 8-polytope, constructed within the symmetry of the E8 group. Its Coxeter symbol is 241, describing its
2_41_polytope
Uniform 7-dimensional polytope
In 7-dimensional geometry, the 321 polytope is a uniform 7-polytope, constructed within the symmetry of the E7 group. It was discovered by Thorold Gosset
3_21_polytope
Topics referred to by the same term
E7, E07, E-7 or E7 may refer to: E7 liquid crystal mixture E7, the Lie group in mathematics E7 polytope, in geometry E7 papillomavirus protein E7 European
E7
Four-dimensional geometric object with flat sides
In geometry, a 4-polytope (sometimes also called a polychoron, polycell, or polyhedroid) is a four-dimensional polytope. It is a connected and closed figure
4-polytope
Regular polytope dual to the hypercube in any number of dimensions
In geometry, a cross-polytope, hyperoctahedron, orthoplex, staurotope, or cocube is a regular, convex polytope that exists in n-dimensional Euclidean
Cross-polytope
Uniform 8 dimensional polytope
for E8: E7, E6, B8, B7, [24] are not shown for being too large to display, but projections in E7 and E6 Coxeter planes can be seen at E8 polytope § Graphs
1_42_polytope
A polytope is a geometric object with flat sides, which exists in any general number of dimensions. The following list of polygons, polyhedra and polytopes
List of polygons, polyhedra and polytopes
List_of_polygons,_polyhedra_and_polytopes
Polytope with highest degree of symmetry
In mathematics, a regular polytope is a polytope whose symmetry group acts transitively on its flags, thus giving it the highest degree of symmetry. In
Regular_polytope
5-dimensional geometric object
geometry, a five-dimensional polytope (or 5-polytope or polyteron) is a polytope in five-dimensional space, bounded by (4-polytope) facets, pairs of which
5-polytope
Uniform 6-polytope
122 polytope is a uniform polytope, constructed from the E6 group. It was first published in E. L. Elte's 1912 listing of semiregular polytopes, named
1_22_polytope
Geometric space with seven dimensions
Coxeter-Dynkin diagram. The 7-demicube is a unique polytope from the D7 family, and 321, 231, and 132 polytopes from the E7 family. The 6-sphere or hypersphere in
Seven-dimensional_space
5-dimensional hypercube
deleting alternating vertices of the 5-cube, creates another uniform 5-polytope, called a 5-demicube, which is also part of an infinite family called the
5-cube
255 polytopes can be made in the E8, E7, E6, D7, D6, D5, D4, D3, A7, A5 Coxeter planes. Ak has [k+1] symmetry, Dk has [2(k-1)] symmetry, and E6, E7, E8
E8_polytope
10-dimensional hypercube
as a 10 dimensional polytope, constructed from 20 regular facets. Acronym: deker It is a part of an infinite family of polytopes, called hypercubes. The
10-cube
cell of the E7* lattice is the 132 polytope, and voronoi tessellation the 133 honeycomb. The E7* lattice is constructed by 2 copies of the E7 lattice vertices
3_31_honeycomb
6-dimensional geometry, there are 39 uniform polytopes with E6 symmetry. The two simplest forms are the 221 and 122 polytopes, composed of 27 and 72 vertices respectively
E6_polytope
Four-dimensional analogue of the cube
labels it the γ4 polytope. The term hypercube without a dimension reference is frequently treated as a synonym for this specific polytope. The construction
Tesseract
6-dimensional geometric object
six-dimensional geometry, a six-dimensional polytope or 6-polytope is a polytope, bounded by 5-polytope facets. A 6-polytope is a closed six-dimensional figure
6-polytope
Distance-regular graph with 56 vertices
group E7 and hence has order 2903040. The Gosset 321 polytope is a semiregular polytope. Therefore, the automorphism group of the Gosset graph, E7, acts
Gosset_graph
regular polytopes in Euclidean, spherical and hyperbolic spaces. This table shows a summary of regular polytope counts by rank. There is only one polytope of
List_of_regular_polytopes
133-dimensional exceptional simple Lie group
In mathematics, E7 is the name of several closely related Lie groups, linear algebraic groups or their Lie algebras e7, all of which have dimension 133;
E7_(mathematics)
Isogonal polytope with uniform facets
In geometry, a uniform polytope of dimension three or higher is a vertex-transitive polytope bounded by uniform facets. Here, "vertex-transitive" means
Uniform_polytope
Uniform polychoron
In four-dimensional geometry, the rectified 5-cell is a uniform 4-polytope composed of 5 regular tetrahedral and 5 regular octahedral cells. Each edge
Rectified_5-cell
7-dimensional hypercube
called a regular tetradeca-7-tope or tetradecaexon, being a 7 dimensional polytope constructed from 14 regular facets. This configuration matrix represents
7-cube
Polytope contained by 7-polytope facets
eight-dimensional polytope or 8-polytope is a polytope contained by 7-polytope facets, each 6-polytope ridge being shared by exactly two 7-polytope facets. A
Uniform_8-polytope
five-dimensional geometry, a rectified 5-simplex is a convex uniform 5-polytope, being a rectification of the regular 5-simplex. There are three unique
Rectified_5-simplexes
Uniform 6-polytope
In 6-dimensional geometry, the 221 polytope is a uniform 6-polytope, constructed within the symmetry of the E6 group. It was discovered by Thorold Gosset
2_21_polytope
Class of 4-dimensional polytopes
In geometry, a uniform 4-polytope (or uniform polychoron) is a 4-dimensional polytope which is vertex-transitive and whose cells are uniform polyhedra
Uniform_4-polytope
Regular 5-polytope
five-dimensional geometry, a demipenteract or 5-demicube is a semiregular 5-polytope, constructed from a 5-hypercube (penteract) with alternated vertices removed
5-demicube
9-dimensional hypercube
nine-dimensional polytope constructed with 18 regular facets. It was given acronym enne by J. Bowers. It is a part of an infinite family of polytopes, called hypercubes
9-cube
Four-dimensional analogue of the tetrahedron
In geometry, the 5-cell is the convex 4-polytope with Schläfli symbol {3,3,3}. It is a 5-vertex four-dimensional object bounded by five tetrahedral cells
5-cell
Five-dimensional geometric shape
5-polytope is a five-dimensional uniform polytope. By definition, a uniform 5-polytope is vertex-transitive and constructed from uniform 4-polytope facets
Uniform_5-polytope
Uniform 6-dimensional polytope
uniform 6-polytope is a six-dimensional uniform polytope. A uniform polypeton is vertex-transitive, and all facets are uniform 5-polytopes. The complete
Uniform_6-polytope
Type of geometrical object
geometry, a 10-polytope is a 10-dimensional polytope whose boundary consists of 9-polytope facets, exactly two such facets meeting at each 8-polytope ridge. A
Uniform_10-polytope
Convex regular 5-polytope in geometry
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
5-orthoplex
Multi-dimensional generalization of triangle
dimensions. The simplex is so-named because it represents the simplest possible polytope in any given dimension. For example, a 0-dimensional simplex is a point
Simplex
Uniform 6-polytope
6-polytope, constructed from a 6-cube (hexeract) with alternated vertices removed. It is part of a dimensionally infinite family of uniform polytopes called
6-demicube
6-dimensional hypercube
being a 6-dimensional polytope constructed from 12 regular facets. Acronym: ax It is a part of an infinite family of polytopes, called hypercubes. The
6-cube
In geometry, an E9 honeycomb is a tessellation of uniform polytopes in hyperbolic 9-dimensional space. T ¯ 9 {\displaystyle {\bar {T}}_{9}} , also (E10)
E9_honeycomb
Regular polytope whose 2D form is a pentagon
In geometry, a pentagonal polytope is a regular polytope in n dimensions constructed from the Hn Coxeter group. The family was named by H. S. M. Coxeter
Pentagonal_polytope
Geometric object
geometry, a uniform k21 polytope is a polytope in k + 4 dimensions constructed from the En Coxeter group, and having only regular polytope facets. The family
Uniform_k_21_polytope
Uniform 10-polytope
uniform 10-polytope, constructed from the 10-cube with alternated vertices removed. It is part of a dimensionally infinite family of uniform polytopes called
10-demicube
Convex regular polytope in 10 dimensional geometry
In geometry, a 10-orthoplex or 10-cross polytope, is a regular 10-polytope with 20 vertices, 180 edges, 960 triangle faces, 3360 tetrahedron cells, 8064
10-orthoplex
Uniform 6-polytope
In geometry, a 6-simplex is a self-dual regular 6-polytope. It has 7 vertices, 21 edges, 35 triangle faces, 35 tetrahedral cells, 21 5-cell 4-faces, and
6-simplex
Four-dimensional geometric objects
In 4-dimensional geometry, there are 15 uniform polytopes with H4 symmetry. Two of these, the 120-cell and 600-cell, are regular. Each can be visualized
H4_polytope
In five-dimensional geometry, a stericated 5-cube is a convex uniform 5-polytope with fourth-order truncations (sterication) of the regular 5-cube. There
Stericated_5-cubes
Convex regular 8-polytope
In geometry, an 8-simplex is a self-dual regular 8-polytope. It has 9 vertices, 36 edges, 84 triangle faces, 126 tetrahedral cells, 126 5-cell 4-faces
8-simplex
Type of geometric object
nine-dimensional polytope or 9-polytope is a polytope contained by 8-polytope facets. Each 7-polytope ridge being shared by exactly two 8-polytope facets. A
Uniform_9-polytope
Four-dimensional analog of the octahedron
convex 4-polytope (four-dimensional analogue of a Platonic solid) with Schläfli symbol {3,3,4}. It is one of the six regular convex 4-polytopes first described
16-cell
Polyhedron with four faces
tetrahedron of the cube is an example of a Heronian tetrahedron. Every regular polytope, including the regular tetrahedron, has its characteristic orthoscheme
Tetrahedron
Convex polytope, the n-dimensional analogue of a square and a cube
measure polytope (originally from Elte, 1912) is also used, notably in the work of H. S. M. Coxeter who also labels the hypercubes the γn polytopes. The
Hypercube
Uniform 7-polytope
In geometry, a demihepteract or 7-demicube is a uniform 7-polytope, constructed from the 7-hypercube (hepteract) with alternated vertices removed. It is
7-demicube
Regular 6 dimensional polytope
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
6-orthoplex
Type of 7-polytope
In 7-dimensional geometry, a 7-simplex is a self-dual regular 7-polytope. It has 8 vertices, 28 edges, 56 triangle faces, 70 tetrahedral cells, 56 5-cell
7-simplex
In 7-dimensional geometry, there are 128 uniform polytopes with B7 symmetry. There are two regular forms, the 7-orthoplex, and 8-cube with 14 and 128
B7_polytope
In geometry, a truncated 5-cell is a uniform 4-polytope (4-dimensional uniform polytope) formed as the truncation of the regular 5-cell. There are two
Truncated_5-cell
248-dimensional exceptional simple Lie group
series labeled An, Bn, Cn, Dn, and five exceptional cases labeled G2, F4, E6, E7, and E8. The E8 algebra is the largest and most complicated of these exceptional
E8_(mathematics)
a runcinated 120-cell (or runcinated 600-cell) is a convex uniform 4-polytope, being a runcination (a 3rd order truncation) of the regular 120-cell.
Runcinated_120-cells
the rectified 600-cell or rectified hexacosichoron is a convex uniform 4-polytope composed of 600 regular octahedra and 120 icosahedra cells. Each edge has
Rectified_600-cell
In 5-dimensional geometry, there are 19 uniform polytopes with A5 symmetry. There is one self-dual regular form, the 5-simplex with 6 vertices. Each can
A5_polytope
Uniform polytope
In geometry, 1k2 polytope is a uniform polytope in n dimensions (n = k + 4) constructed from the En Coxeter group. The family was named by their Coxeter
Uniform_1_k2_polytope
8-dimensional hypercube
hexadecazetton, being an 8-dimensional polytope constructed from 16 regular facets. It is a part of an infinite family of polytopes, called hypercubes. The dual
8-cube
In seven-dimensional geometry, a pentic 7-cube is a convex uniform 7-polytope, related to the uniform 7-demicube. There are 8 unique forms. Small cellated
Pentic_7-cubes
Equiangular and equilateral polygon
Polyhedra? Branko Grünbaum (2003), Fig. 3 Regular polytopes, p.95 Coxeter, The Densities of the Regular Polytopes II, 1932, p.53 Lee, Hwa Young; "Origami-Constructible
Regular_polygon
Group of polytopes
In 8-dimensional geometry, there are 255 uniform polytopes with B8 symmetry (to which this article adds for illustration the 8-demicube as an alternation
B8_polytope
Regular 5-polytope
In five-dimensional geometry, a 5-simplex is a self-dual regular 5-polytope. It has six vertices, 15 edges, 20 triangle faces, 15 tetrahedral cells, and
5-simplex
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. There
Runcinated_24-cells
Convex regular 8-polytope
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-cell
8-orthoplex
nodes: The E7* lattice (also called E72) has double the symmetry, represented by [[3,33,3]]. The Voronoi cell of the E7* lattice is the 132 polytope, and voronoi
1_33_honeycomb
eight-dimensional geometry, a truncated 8-simplex is a convex uniform 8-polytope, being a truncation of the regular 8-simplex. There are four unique degrees
Truncated_8-simplexes
geometry, the snub 24-cell or snub disicositetrachoron is a convex uniform 4-polytope composed of 120 regular tetrahedral and 24 icosahedral cells. Five tetrahedra
Snub_24-cell
Skew polygon derived from a polytope
In geometry, a Petrie polygon for a regular polytope of n dimensions is a skew polygon in which every n – 1 consecutive sides (but no n) belongs to one
Petrie_polygon
eight-dimensional geometry, a heptellated 8-simplex is a convex uniform 8-polytope, including 7th-order truncations (heptellation) from the regular 8-simplex
Heptellated_8-simplexes
geometry, a truncated 6-cube (or truncated hexeract) is a convex uniform 6-polytope, being a truncation of the regular 6-cube. There are 5 truncations for
Truncated_6-cubes
Uniform polytopes with D8 symmetry
In 8-dimensional geometry, there are 191 uniform polytopes with D8 symmetry, of which 64 are unique and 127 are shared with the B8 symmetry. There is
D8_polytope
Regular Schläfli-Hess 4-polytope with 600 vertices
polydodecahedron is a regular star 4-polytope with Schläfli symbol {5/2,3,3}, one of 10 regular Schläfli-Hess 4-polytopes. It is unique among the 10 for having
Great grand stellated 120-cell
Great_grand_stellated_120-cell
In 6-dimensional geometry, there are 47 uniform polytopes with D6 symmetry, of which 16 are unique and 31 are shared with the B6 symmetry. There are two
D6_polytope
convex uniform 5-polytope, being a rectification of the regular 5-orthoplex. There are 5 degrees of rectifications for any 5-polytope, the zeroth here
Rectified_5-orthoplexes
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
Stericated_6-cubes
Convex uniform 7-polytope in seven-dimensional geometry
seven-dimensional geometry, a rectified 7-simplex is a convex uniform 7-polytope, being a rectification of the regular 7-simplex. There are four unique
Rectified_7-simplexes
In nine-dimensional geometry, a rectified 9-cube is a convex uniform 9-polytope, being a rectification of the regular 9-cube. There are 9 rectifications
Rectified_9-cubes
Regular object in four dimensional geometry
In four-dimensional geometry, the 24-cell is a convex regular 4-polytope, a four-dimensional analogue of a Platonic solid. It is named for the 24 octahedra
24-cell
convex uniform 8-polytope, being a rectification of the regular 8-simplex. There are unique 3 degrees of rectifications in regular 8-polytopes. Vertices of
Rectified_8-simplexes
nine-dimensional geometry, a rectified 9-simplex is a convex uniform 9-polytope, being a rectification of the regular 9-orthoplex. There are 9 rectifications
Rectified_9-orthoplexes
five-dimensional geometry, a stericated 5-simplex is a convex uniform 5-polytope with fourth-order truncations (sterication) of the regular 5-simplex. There
Stericated_5-simplexes
Regular 7- polytope
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-cell
7-orthoplex
Type of 7-polytope
seven-dimensional geometry, a hexicated 7-simplex is a convex uniform 7-polytope, including 6th-order truncations (hexication) from the regular 7-simplex
Hexicated_7-simplexes
In six-dimensional geometry, a runcic 6-cube is a convex uniform 6-polytope. There are 2 unique runcic for the 6-cube. Cantellated 6-demicube Cantellated
Runcic_6-cubes
In 5-dimensional geometry, there are 31 uniform polytopes with B5 symmetry. There are two regular forms, the 5-orthoplex, and 5-cube with 10 and 32 vertices
B5_polytope
Four-dimensional analog of the dodecahedron
In geometry, the 120-cell is the convex regular 4-polytope (four-dimensional analogue of a Platonic solid) with Schläfli symbol {5,3,3}. It is also called
120-cell
In seven-dimensional geometry, a hexic 7-cube is a convex uniform 7-polytope, constructed from the uniform 7-demicube. There are 16 unique forms. Small
Hexic_7-cubes
a stericated 7-cube (or runcinated 7-demicube) is a convex uniform 7-polytope, being a runcination of the uniform 7-demicube. There are 4 unique runcinations
Steric_7-cubes
six-dimensional geometry, a truncated 6-simplex is a convex uniform 6-polytope, being a truncation of the regular 6-simplex. There are unique 3 degrees
Truncated_6-simplexes
seven-dimensional geometry, a runcinated 7-cube is a convex uniform 7-polytope with 3rd order truncations (runcination) of the regular 7-cube. There are
Runcinated_7-cubes
E7 POLYTOPE
E7 POLYTOPE
E7 POLYTOPE
E7 POLYTOPE
Female
Dutch
, war refuge.
Boy/Male
Sikh
One who delights in devotion to God
Girl/Female
Tamil
Ananda Lakshmi | ஆநஂதாலகà¯à®·à¯à®®à¯€
Goddess of happiness
Girl/Female
Muslim
Inception, Foundation
Surname or Lastname
English (chiefly Yorkshire)
English (chiefly Yorkshire) : variant spelling of Morehouse.
Girl/Female
Arabic
Beautiful; Pretty
Surname or Lastname
English
English : from an Old Breton personal name, derived from an element meaning ‘high’, ‘mighty’, which was introduced into England by followers of William the Conqueror and subsequently into Ireland, where it still has some currency as a personal name.Scottish : habitational name from a place in Kincardineshire. The place name is of uncertain origin, possibly from an early Celtic name, Conona ‘hound stream’.Roger Conant led a secession from Plymouth colony in about 1627 and founded the settlement that became Salem, MA. He was probably the son of Christopher Connant, who came over from England aboard the Anne in 1623.
Male
German
German form of French Percevel, PARZIVAL means "pierced valley."
Boy/Male
Hindu, Indian
Fish
Boy/Male
Arabic, Muslim
The Truthful (One) to Allah; An Epithet of Prophet Yusuf
E7 POLYTOPE
E7 POLYTOPE
E7 POLYTOPE
E7 POLYTOPE
E7 POLYTOPE