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In 4-dimensional geometry, there are 15 uniform 4-polytopes with B4 symmetry. There are two regular forms, the tesseract and 16-cell, with 16 and 8 vertices
B4_polytope
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
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
Four-dimensional analogue of the cube
the tesseract's defining symmetry group, the group which generates the B4 polytopes. The tesseract's characteristic simplex directly generates the tesseract
Tesseract
Four-dimensional analogues of the regular polyhedra in three dimensions
In mathematics, a regular 4-polytope or regular polychoron is a regular four-dimensional polytope. They are the four-dimensional analogues of the regular
Regular_4-polytope
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
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
Uniform 8 dimensional polytope
In 8-dimensional geometry, the 142 is a uniform 8-polytope, constructed within the symmetry of the E8 group. Its Coxeter symbol is 142, describing its
1_42_polytope
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
there are 7 uniform 4-polytopes with reflections of D4 symmetry, all are shared with higher symmetry constructions in the B4 or F4 symmetry families
D4_polytope
Generalization of a polytope in real space
In geometry, a complex polytope is a generalization of a polytope in real space to an analogous structure in a complex Hilbert space, where each real dimension
Complex_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
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
a semiregular polytope, labeling it as tC24. It can also be considered a cantellated 16-cell with the lower symmetries B4 = [3,3,4]. B4 would lead to
Rectified_24-cell
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
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
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
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
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
truncated 24-cell can be constructed from polytopes with three symmetry groups: F4 [3,4,3]: A truncation of the 24-cell. B4 [3,3,4]: A cantitruncation of the
Truncated_24-cells
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
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
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
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
Convex regular 9 dimensional polytope
In geometry, a 9-orthoplex or 9-cross polytope, is a regular 9-polytope with 18 vertices, 144 edges, 672 triangle faces, 2016 tetrahedron cells, 4032
9-orthoplex
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
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
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
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
these 64 polytopes can be made in the B6, B5, B4, B3, B2, A5, A3, Coxeter planes. Ak has [k+1] symmetry, and Bk has [2k] symmetry. These 64 polytopes are each
B6_polytope
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
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
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
a runcinated tesseract (or runcinated 16-cell) is a convex uniform 4-polytope, being a runcination (a 3rd order truncation) of the regular tesseract
Runcinated_tesseracts
Type of tesseract
In geometry, a truncated tesseract is a uniform 4-polytope formed as the truncation of the regular tesseract. There are three truncations, including a
Truncated_tesseract
seven-dimensional geometry, a stericated 7-cube is a convex uniform 7-polytope with 4th-order truncations (sterication) of the regular 7-cube. There are
Stericated_7-cubes
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
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
these 32 polytopes can be made in the B5, B4, B3, B2, A3, Coxeter planes. Ak has [k+1] symmetry, and Bk has [2k] symmetry. These 32 polytopes are each
B5_polytope
seven-dimensional geometry, a stericated 7-orthoplex is a convex uniform 7-polytope with 4th order truncations (sterication) of the regular 7-orthoplex. There
Stericated_7-orthoplexes
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
Group of polytopes
subgroups. Symmetric orthographic projections of these 256 polytopes can be made in the B8, B7, B6, B5, B4, B3, B2, A7, A5, A3, Coxeter planes. Ak has [k+1] symmetry
B8_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
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
seven-dimensional geometry, a pentellated 7-orthoplex is a convex uniform 7-polytope with 5th order truncations (pentellation) of the regular 7-orthoplex. There
Pentellated_7-orthoplexes
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
Stericated_6-orthoplexes
In 4-dimensional geometry, there are 9 uniform 4-polytopes with F4 symmetry, and one chiral half symmetry, the snub 24-cell. There is one self-dual regular
List_of_F4_polytopes
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
seven-dimensional geometry, a pentellated 7-cube is a convex uniform 7-polytope with 5th order truncations (pentellation) of the regular 7-cube. There
Pentellated_7-cubes
128 polytopes can be made in the B7, B6, B5, B4, B3, B2, A5, A3, Coxeter planes. Ak has [k+1] symmetry, and Bk has [2k] symmetry. These 128 polytopes are
B7_polytope
In five-dimensional geometry, a truncated 5-cube is a convex uniform 5-polytope, being a truncation of the regular 5-cube. There are four unique truncations
Truncated_5-cubes
Uniform 7- polytope
In seven-dimensional geometry, a truncated 7-cube is a convex uniform 7-polytope, being a truncation of the regular 7-cube. There are 6 truncations for
Truncated_7-cubes
Convex uniform 8-polytope in 8-dimensional geometry
In eight-dimensional geometry, a truncated 8-cube is a convex uniform 8-polytope, being a truncation of the regular 8-cube. There are unique 7 degrees of
Truncated_8-cubes
In ten-dimensional geometry, a rectified 10-cube is a convex uniform 10-polytope, being a rectification of the regular 10-cube. There are 10 rectifications
Rectified_10-cubes
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
eight-dimensional geometry, a rectified 8-orthoplex is a convex uniform 8-polytope, being a rectification of the regular 8-orthoplex. There are unique 8 degrees
Rectified_8-orthoplexes
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
is a convex uniform 5-polytope, being a rectification of the regular 5-cube. There are 5 degrees of rectifications of a 5-polytope, the zeroth here being
Rectified_5-cubes
In seven-dimensional geometry, a rectified 7-cube is a convex uniform 7-polytope, being a rectification of the regular 7-cube. There are unique 7 degrees
Rectified_7-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
Stericated_6-cubes
the rectified tesseract, rectified 8-cell is a uniform 4-polytope (4-dimensional polytope) bounded by 24 cells: 8 cuboctahedra, and 16 tetrahedra. It
Rectified_tesseract
four-dimensional geometry, a cantellated 24-cell is a convex uniform 4-polytope, being a cantellation (a 2nd order truncation) of the regular 24-cell.
Cantellated_24-cells
Geometric space with four dimensions
both synthetic and algebraic methods. He discovered all of the regular polytopes (higher-dimensional analogues of the Platonic solids) that exist in Euclidean
Four-dimensional_space
Geometrical Shape
In six-dimensional geometry, a rectified 6-cube is a convex uniform 6-polytope, being a rectification of the regular 6-cube. There are unique 6 degrees
Rectified_6-cubes
eight-dimensional geometry, a truncated 8-orthoplex is a convex uniform 8-polytope, being a truncation of the regular 8-orthoplex. There are 7 truncation
Truncated_8-orthoplexes
7-polytope
seven-dimensional geometry, a truncated 7-orthoplex is a convex uniform 7-polytope, being a truncation of the regular 7-orthoplex. There are 6 truncations
Truncated_7-orthoplexes
six-dimensional geometry, a cantellated 6-orthoplex is a convex uniform 6-polytope, being a cantellation of the regular 6-orthoplex. There are 8 cantellation
Cantellated_6-orthoplexes
Four-dimensional analog of the icosahedron
In geometry, the 600-cell is the convex regular 4-polytope (four-dimensional analogue of a Platonic solid) with Schläfli symbol {3,3,5}. It is also known
600-cell
six-dimensional geometry, a truncated 6-orthoplex is a convex uniform 6-polytope, being a truncation of the regular 6-orthoplex. There are 5 degrees of
Truncated_6-orthoplexes
five-dimensional geometry, a truncated 5-orthoplex is a convex uniform 5-polytope, being a truncation of the regular 5-orthoplex. There are 4 unique truncations
Truncated_5-orthoplexes
Pictorial representation of symmetry
(called branches) representing a Coxeter group or sometimes a uniform polytope or uniform tiling constructed from the group. A class of closely related
Coxeter–Dynkin_diagram
five-dimensional geometry, a runcinated 5-orthoplex is a convex uniform 5-polytope with 3rd order truncation (runcination) of the regular 5-orthoplex. There
Runcinated_5-orthoplexes
ten-dimensional geometry, a rectified 10-orthoplex is a convex uniform 10-polytope, being a rectification of the regular 10-orthoplex. There are 10 rectifications
Rectified_10-orthoplexes
seven-dimensional geometry, a runcinated 7-orthoplex is a convex uniform 7-polytope with 3rd order truncations (runcination) of the regular 7-orthoplex. There
Runcinated_7-orthoplexes
In five-dimensional geometry, a runcinated 5-cube is a convex uniform 5-polytope that is a runcination (a 3rd order truncation) of the regular 5-cube. There
Runcinated_5-cubes
Group that admits a formal description in terms of reflections
Examples of finite Coxeter groups include the symmetry groups of regular polytopes, and the Weyl groups of simple Lie algebras. Examples of infinite Coxeter
Coxeter_group
seven-dimensional geometry, a cantellated 7-orthoplex is a convex uniform 7-polytope, being a cantellation of the regular 7-orthoplex. There are ten degrees
Cantellated_7-orthoplexes
Convex uniform 4-polytope
four-dimensional geometry, a cantellated tesseract is a convex uniform 4-polytope, being a cantellation (a 2nd order truncation) of the regular tesseract
Cantellated_tesseract
In six-dimensional geometry, a runcinated 6-cube is a convex uniform 6-polytope with 3rd order truncations (runcination) of the regular 6-cube. There are
Runcinated_6-cubes
honeycomb. Its vertex figure is a 24-cell. The vertex arrangement is called the B4, D4, or F4 lattice. Hexadecachoric tetracomb/honeycomb Demitesseractic tetracomb/honeycomb
16-cell_honeycomb
six-dimensional geometry, a runcinated 6-orthplex is a convex uniform 6-polytope with 3rd order truncations (runcination) of the regular 6-orthoplex. There
Runcinated_6-orthoplexes
seven-dimensional geometry, a rectified 7-orthoplex is a convex uniform 7-polytope, being a rectification of the regular 7-orthoplex. There are unique 7 degrees
Rectified_7-orthoplexes
In six-dimensional geometry, a cantellated 5-cube is a convex uniform 5-polytope, being a cantellation of the regular 5-cube. There are 6 unique cantellation
Cantellated_5-cubes
five-dimensional geometry, a cantellated 5-orthoplex is a convex uniform 5-polytope, being a cantellation of the regular 5-orthoplex. There are 6 cantellation
Cantellated_5-orthoplexes
Concept in euclidean geometry
order-3 tesseractic honeycomb. It is topologically equivalent to the regular polytope penteract in 5-space. The tesseract can make a regular tessellation of
Tesseractic_honeycomb
In six-dimensional geometry, a cantellated 6-cube is a convex uniform 6-polytope, being a cantellation of the regular 6-cube. There are 8 cantellations
Cantellated_6-cubes
seven-dimensional geometry, a cantellated 7-cube is a convex uniform 7-polytope, being a cantellation of the regular 7-cube. There are 10 degrees of cantellation
Cantellated_7-cubes
In eight-dimensional geometry, a rectified 8-cube is a convex uniform 8-polytope, being a rectification of the regular 8-cube. There are unique 8 degrees
Rectified_8-cubes
a hexicated 7-orthoplex (also hexicated 7-cube) is a convex uniform 7-polytope, including 6th-order truncations (hexication) from the regular 7-orthoplex
Hexicated_7-orthoplexes
four-dimensional crystal classes 1985 H.S.M. Coxeter, Regular and Semi-Regular Polytopes II, Coxeter notation for 4D point groups 2003 John Conway and Smith, On
Point groups in four dimensions
Point_groups_in_four_dimensions
six-dimensional geometry, a rectified 6-orthoplex is a convex uniform 6-polytope, being a rectification of the regular 6-orthoplex. There are unique 6 degrees
Rectified_6-orthoplexes
Polygon shape with eight sides
these higher-dimensional regular and uniform polytopes, shown in these skew orthogonal projections of in A7, B4, and D5 Coxeter planes. The regular octagon
Octagon
Prime number of the form 2^n – 1
geometry, the number of polytopes that are part of the family of polytopes formed by a truncation operation of a base regular polytope and its dual (excluding
Mersenne_prime
Coxeter, Complex Regular polytopes, p. 117, 132 Coxeter, Regular Complex Polytopes, p. 109 Shephard, G.C.; Regular complex polytopes, Proc. London math. Soc
Möbius–Kantor_polygon
Pictorial representation of symmetry
hexagonal lattice. An associated polytope – for example Gosset 421 polytope may be referred to as "the E8 polytope", as its vertices are derived from
Dynkin_diagram
Polygonal chain whose vertices are not all coplanar
Regular complex polytopes, p. 6 Abstract Regular Polytopes, p.217 McMullen, Peter; Schulte, Egon (December 2002), Abstract Regular Polytopes (1st ed.), Cambridge
Skew_polygon
Concept in geometry
used to draw diagrams of higher-dimensional polytopes and root systems – the vertices and edges of the polytope, or roots (and some edges connecting these)
Coxeter_element
Mathematical model of the physical space
polytopes, which are the higher-dimensional analogues of polygons and polyhedra. He developed their theory and discovered all the regular polytopes,
Euclidean_geometry
Tessalating shape in four dimensional space
honeycomb Omnitruncated 5-cell honeycomb Coxeter, Regular and Semi-Regular Polytopes III, (1988), p318 Kaleidoscopes: Selected Writings of H. S. M. Coxeter
Rectified tesseractic honeycomb
Rectified_tesseractic_honeycomb
the Wayback Machine (Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3-45] See p318 [2] George Olshevsky, Uniform
Cantellated tesseractic honeycomb
Cantellated_tesseractic_honeycomb
B4 POLYTOPE
B4 POLYTOPE
B4 POLYTOPE
B4 POLYTOPE
Surname or Lastname
English
English : topographic name for someone living on the banks of any of the several rivers so called. The river name is of British origin; it may be composed of the unattested elements tri ‘through’, ‘across’ + sant- ‘travel’, ‘journey’; alternatively it may mean ‘traveler’ or ‘trespasser’, a reference to frequent flooding. There is a village in Dorset of this name, on the river Trent or Piddle, and the surname may therefore also be a habitational name derived from this.Scottish : probably of the same origin as 1, though in some cases it may be from a reduced form of Tranent, a place in East Lothian.
Girl/Female
Latin
Announces.
Boy/Male
Indian, Sanskrit
Loved by Everyone
Girl/Female
Biblical
Bag of flax or linen.
Boy/Male
Tamil
Navakanth | நாவாகாஂத
New light
Boy/Male
British, English
Happy
Girl/Female
English
Temperance. One of the qualities adopted as a first name by the Puritans after the Reformation.
Boy/Male
Indian
Another name of God, Exalted, Tall
Boy/Male
Hindu, Indian
Wearing Yellow
Girl/Female
Bengali, Hindu, Indian, Kannada, Malayalam, Marathi, Telugu
Sacred River; Good Smell
B4 POLYTOPE
B4 POLYTOPE
B4 POLYTOPE
B4 POLYTOPE
B4 POLYTOPE