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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
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 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
Uniform 7-polytope
There are 95 uniform polytopes with D6 symmetry, 63 are shared by the B6 symmetry, and 32 are unique: Coxeter, Regular Polytopes, sec 1.8 Configurations
7-demicube
Uniform 6-polytope
subgroup order by removing one mirror at a time. There are 47 uniform polytopes with D6 symmetry, 31 are shared by the B6 symmetry, and 16 are unique: The
6-demicube
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
Icosidodecahedron from D6 John Baez, January 1, 2015 Klitzing, (o3o3x3o3o4o - brag). H.S.M. Coxeter: H.S.M. Coxeter, Regular Polytopes, 3rd edition, Dover
Rectified_6-orthoplexes
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
subgroups. Symmetric orthographic projections of these 255 polytopes can be made in the E8, E7, E6, D7, D6, D5, D4, D3, A7, A5 Coxeter planes. Ak has [k+1] symmetry
E8_polytope
±3,±5,±7) with an odd number of plus signs. There are 47 uniform polytopes with D6 symmetry, 31 are shared by the B6 symmetry, and 16 are unique: Klitzing
Steric_6-cubes
for being alternation of the hypercube family. There are 47 uniform polytopes with D6 symmetry, 31 are shared by the B6 symmetry, and 16 are unique: Klitzing
Runcic_6-cubes
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
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
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
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
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
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
planes of the D6 Coxeter group, and other subgroups. Symmetric orthographic projections of these 32 polytopes can be made in the D7, D6, D5, D4, D3, A5
D7_polytope
Uniform polytopes with D8 symmetry
subgroups. Symmetric orthographic projections of these 64 polytopes can be made in the D8, D7, D6, D5, D4, D3, A7, A5, A3, Coxeter planes. Ak has [k+1] symmetry
D8_polytope
Geometric space with six dimensions
Coxeter–Dynkin diagram. The 6-demicube is a unique polytope from the D6 family, and 221 and 122 polytopes from the E6 family. The 5-sphere, or hypersphere
Six-dimensional_space
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
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
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
±3,±5,±7) with an odd number of plus signs. There are 47 uniform polytopes with D6 symmetry, 31 are shared by the B6 symmetry, and 16 are unique: Klitzing
Pentic_6-cubes
subgroups. Symmetric orthographic projections of these 127 polytopes can be made in the E7, E6, D6, D5, D4, D3, A6, A5, A4, A3, A2 Coxeter planes. Ak has
E7_polytope
here shown with red color for no overlaps. There are 95 uniform polytopes with D6 symmetry, 63 are shared by the B6 symmetry, and 32 are unique: Klitzing
Cantic_7-cube
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
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
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
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
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
Shape in six-dimensional geometry
±3,±3,±3) with an odd number of plus signs. There are 47 uniform polytopes with D6 symmetry, 31 are shared by the B6 symmetry, and 16 are unique: Klitzing
Cantic_6-cube
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
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
Uniform 4-polytope
In geometry, a tetrahedral prism is a convex uniform 4-polytope. This 4-polytope has 6 polyhedral cells: 2 tetrahedra connected by 4 triangular prisms
Tetrahedral_prism
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
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
Isogonal polyhedron with regular faces
polyhedron is a 2-dimensional abstract polytope with a non-degenerate 3-dimensional realization. Here an abstract polytope is a poset of its "faces" satisfying
Uniform_polyhedron
Uniform 9-polytope
uniform 9-polytope, constructed from the 9-cube, with alternated vertices removed. It is part of a dimensionally infinite family of uniform polytopes called
9-demicube
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
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
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
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
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
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
Uniform 8-polytope
eight-dimensional geometry, a cantic 8-cube or truncated 8-demicube is a uniform 8-polytope, being a truncation of the 8-demicube. Truncated demiocteract Truncated
Cantic_8-cube
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
Uniform 8 dimensional polytope
In geometry, a demiocteract or 8-demicube is a uniform 8-polytope, constructed from the 8-hypercube, octeract, with alternated vertices removed. It is
8-demicube
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
Shape with six sides
symmetry), making up the dihedral group D6. There are 16 subgroups. There are 8 up to isomorphism: itself (D6), 2 dihedral: (D3, D2), 4 cyclic: (Z6, Z3
Hexagon
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
3,3,4} facets. The vertex arrangement of the 6-demicubic honeycomb is the D6 lattice. The 60 vertices of the rectified 6-orthoplex vertex figure of the
6-demicubic_honeycomb
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
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
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
Polyhedron with non-planar faces
ISBN 978-0-521-81496-6. Chapter I Classical Regular Polytopes (Sample text) Coxeter, Regular and Semi-Regular Polytopes II, 2.34 Coxeter and Moser, Generators and
Regular_skew_polyhedron
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
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
In seven-dimensional geometry, a runcic 7-cube is a convex uniform 7-polytope, related to the uniform 7-demicube. There are 2 unique forms. A runcic 7-cube
Runcic_7-cubes
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
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
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
Group of irregular uniform polytopes
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
Gosset–Elte_figures
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
Regular Polytopes I, [Math. Zeit. 46 (1940) 380-407, MR 2,10] (1.9 Uniform space-fillings) (Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III
Cyclotruncated 5-simplex honeycomb
Cyclotruncated_5-simplex_honeycomb
Group of geometric symmetries with at least one fixed point
polyhedral groups of 3D, it can be named by its related convex regular 4-polytope. Related pure rotational groups exist for each with half the order, and
Point_group
Regular Polytopes I, [Math. Zeit. 46 (1940) 380–407, MR 2,10] (1.9 Uniform space-fillings) (Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III
5-simplex_honeycomb
This makes the tetrahedral duoprism, {3,3}×{3,3}. Each vertex of this polytope corresponds to the center of a 6-sphere in a moderately dense sphere packing
1_33_honeycomb
Undirected graph with 11 nodes and 27 edges
England: Oxford University Press, p. 285. Grünbaum, Branko (1967), Convex Polytopes, Wiley Interscience, p. 357. Same page, 2nd ed., Graduate Texts in Mathematics
Goldner–Harary_graph
Five dimensional space-filling tessellation
Regular Polytopes I, [Math. Zeit. 46 (1940) 380-407, MR 2,10] (1.9 Uniform space-fillings) (Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III
Omnitruncated 5-simplex honeycomb
Omnitruncated_5-simplex_honeycomb
removing the ringed node and ringing the neighboring node. This makes 231 polytope. The edge figure is determined by removing the ringed node and ringing
3_31_honeycomb
Polygon with 12 edges
The regular dodecagon is the Petrie polygon for many higher-dimensional polytopes, seen as orthogonal projections in Coxeter planes. Examples in 4 dimensions
Dodecagon
Graph with a triangular truncated trapezohedron as its skeleton
Campbell, Stephen R.; Plummer, Michael D. (1988), "On well-covered 3-polytopes", Ars Combinatoria, 25 (A): 215–242, MR 0942505. Castagna, Frank; Prins
Dürer_graph
Six-pointed star polygon
Grünbaum, B.; Polyhedra with Hollow Faces, Proc of NATO-ASI Conference on Polytopes ... etc. (Toronto 1993), ed T. Bisztriczky et al., Kluwer Academic (1994)
Hexagram
Shape with ten sides
regular skew decagon is the Petrie polygon for many higher-dimensional polytopes, shown in these orthogonal projections in various Coxeter planes: The
Decagon
honeycomb Omnitruncated 6-simplex honeycomb Coxeter, Regular and Semi-Regular Polytopes III, (1988), p318 Kaleidoscopes: Selected Writings of H. S. M. Coxeter
Quarter_6-cubic_honeycomb
and Semi Regular Polytopes I, [Math. Zeit. 46 (1940) 380–407, MR 2,10] (Paper 23) H.S.M. Coxeter, Regular and Semi-Regular Polytopes II, [Math. Zeit.
List of spherical symmetry groups
List_of_spherical_symmetry_groups
all birectified 6-orthoplex facets and is the Voronoi tessellation of the D6* lattice. Facets can be identically colored from a doubled C ~ 6 {\displaystyle
6-cubic_honeycomb
and Semi Regular Polytopes I, [Math. Zeit. 46 (1940) 380–407, MR 2,10] (Paper 23) H.S.M. Coxeter, Regular and Semi-Regular Polytopes II, [Math. Zeit.
List of planar symmetry groups
List_of_planar_symmetry_groups
Bipartite non-Hamiltonian polyhedral graph
MR 0731570 Grünbaum, Branko (2003), "13.1 Steinitz's theorem", Convex Polytopes, Graduate Texts in Mathematics, vol. 221 (2nd ed.), Springer-Verlag, pp
Herschel_graph
Groups of point isometries in 3 dimensions
85–96, doi:10.1080/17513470701416264, S2CID 40755219 Coxeter, Regular polytopes, §12.6 The number of reflections, equation 12.61 Burban, Igor. "Du Val
Point groups in three dimensions
Point_groups_in_three_dimensions
Classification system for symmetry groups in geometry
elements can be seen in ringed nodes Coxeter-Dynkin diagram for uniform polytopes and honeycomb are related to hole nodes around the + elements, empty circles
Coxeter_notation
D6 POLYTOPE
D6 POLYTOPE
D6 POLYTOPE
D6 POLYTOPE
Male
Dutch
, gifts of Jehovah.
Girl/Female
Arabic
Funny
Boy/Male
Christian & English(British/American/Australian)
Wanderering Noble
Boy/Male
Spanish American
Young lion.
Boy/Male
Muslim
Surname or Lastname
English
English : possibly a habitational name from Belmore Farm in Shropshire, Belmore House in Hampshire, or Bellmoor Farm in Somerset.
Female
French
Medieval French form of English Isolde, ISEULT means "ice battle." In Arthurian legend, this is the name a tragic princess who was the mistress of Tristram.
Boy/Male
Hindu, Indian, Traditional
Flower of Vicotry
Boy/Male
Tamil
Chidanand | சிதாநஂத
Lord Brahma
Boy/Male
Muslim
Slave of the vigilant
D6 POLYTOPE
D6 POLYTOPE
D6 POLYTOPE
D6 POLYTOPE
D6 POLYTOPE