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In 5-dimensional geometry, there are 23 uniform polytopes with D5 symmetry, 8 are unique, and 15 are shared with the B5 symmetry. There are two special
D5_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
Regular 5-polytope
order D5 divided by the symmetry order of the subgroup with selected mirrors removed. It is a part of a dimensional family of uniform polytopes called
5-demicube
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
Convex regular 5-polytope in geometry
the D5 or [32,1,1] Coxeter group, and the final one as a dual 5-orthotope, called a 5-fusil which can have a variety of subsymmetries. This polytope is
5-orthoplex
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
subgroups. Symmetric orthographic projections of these 39 polytopes can be made in the E6, D5, D4, D2, A5, A4, A3 Coxeter planes. Ak has k+1 symmetry,
E6_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
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
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
Geometric space with five dimensions
higher dimensions, including five-dimensional space. List of regular 5-polytopes — regular geometric shapes that exist in five-dimensional space. Four-dimensional
Five-dimensional_space
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
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
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
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
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
Uniform 5-polytope
alternation of the hypercube family. There are 23 uniform 5-polytopes that can be constructed from the D5 symmetry of the 5-demicube, of which are unique to this
Cantic_5-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
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
hypercube family. There are 23 uniform polytera (uniform 5-polytopes) that can be constructed from the D5 symmetry of the 5-demicube, 8 of which are unique to
Steric_5-cubes
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 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
subgroups. Symmetric orthographic projections of these 32 polytopes can be made in the D7, D6, D5, D4, D3, A5, A3, Coxeter planes. Ak has [k+1] symmetry
D7_polytope
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
Concept in geometry
alternation of the hypercube family. There are 23 uniform 5-polytopes that can be constructed from the D5 symmetry of the 5-demicube, of which are unique to this
Runcic_5-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
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
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
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
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 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
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
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
Type of uniform space-filling tessellation
Conway (1998), p. 119 "The Lattice D5". Conway (1998), p. 120 Conway (1998), p. 466 Coxeter, H.S.M. Regular Polytopes, (3rd edition, 1973), Dover edition
5-demicubic_honeycomb
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
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
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 k+1
E7_polytope
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
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 stericated 7-cube is a convex uniform 7-polytope with 4th-order truncations (sterication) of the regular 7-cube. There are
Stericated_7-cubes
subgroups. Symmetric orthographic projections of these 16 polytopes can be made in the D6, D5, D4, D3, A5, A3, Coxeter planes. Ak has [k+1] symmetry, Dk
D6_polytope
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
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
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
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
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
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
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
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
In six-dimensional geometry, a pentic 6-cube is a convex uniform 6-polytope. There are 8 pentic forms of the 6-cube. The pentic 6-cube, , has half of the
Pentic_6-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
uniform 7-polytope, being a truncation of the 7-demicube. A uniform 7-polytope is vertex-transitive and constructed from uniform 6-polytope facets, and
Cantic_7-cube
In six-dimensional geometry, a steric 6-cube is a convex uniform 6-polytope. There are unique 4 steric forms of the 6-cube. Runcinated demihexeract Runcinated
Steric_6-cubes
Prism with a 3-sided base
Schönhardt polyhedron. It has a relationship with the honeycombs and polytopes. It can be found in many real-life applications as in architecture and
Triangular_prism
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 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
Prism with a 5-sided base
group of a right pentagonal prism is D5h of order 20. The rotation group is D5 of order 10. The volume, as for all prisms, is the product of the area of
Pentagonal_prism
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
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
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
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
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 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
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
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
Shape with five sides
Uniform n-polytope n-simplex n-orthoplex • n-cube n-demicube 1k2 • 2k1 • k21 n-pentagonal polytope Topics: Polytope families • Regular polytope • List of
Pentagon
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
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
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
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
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
Type of uniform tessellation
8-simplices. The vertex figure of Gosset's honeycomb is the semiregular 421 polytope. It is the final figure in the k21 family. This honeycomb is highly regular
5_21_honeycomb
birectified 8-simplex vertex figure. It is the final figure in the 1k2 polytope family. It is created by a Wythoff construction upon a set of 9 hyperplane
1_52_honeycomb
Tiling of five-dimensional space
{\displaystyle {\tilde {D}}_{5}} , [31,1,3,31,1] symmetry. List of regular polytopes Regular and uniform honeycombs in 5-space: 5-demicubic honeycomb 5-simplex
5-cubic_honeycomb
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
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
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
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
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
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
Eight-dimensional geometric tessellation
honeycomb is a space-filling uniform tessellation. It is composed of 241 polytope and 8-simplex facets arranged in an 8-demicube vertex figure. It is the
2_51_honeycomb
Antiprism with a five-sided base
antiprism occurs as a constituent element in some higher-dimensional polytopes. Two rings of ten pentagonal antiprisms each bound the hypersurface of
Pentagonal_antiprism
Polygon shape with eight sides
higher-dimensional regular and uniform polytopes, shown in these skew orthogonal projections of in A7, B4, and D5 Coxeter planes. The regular octagon has
Octagon
Shape in six-dimensional geometry
six-dimensional geometry, a cantic 6-cube (or a truncated 6-demicube) is a uniform 6-polytope. Truncated 6-demicube Truncaced demihexeract Truncated hemihexeract (Acronym:
Cantic_6-cube
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
5-orthoplex honeycomb, {3,3,3,4,3}, with 5-orthoplex facets, the regular 4-polytope 24-cell, {3,4,3} with octahedral (3-orthoplex) cell, and cube {4,3}, with
16-cell_honeycomb
6, and 12, which can be seen in projective symmetry of the polytopes. The Witting polytope, 3{3}3{3}3{3}3, contains the Hessian polyhedron as cells and
Hessian_polyhedron
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
&-1\\0&0&-1&2\end{matrix}}\right]} E5 is another name for the Lie algebra D5 of dimension 45, with Cartan determinant 4. [ 2 − 1 0 0 0 − 1 2 − 1 0 0 0
En_(Lie_algebra)
honeycomb Omnitruncated 5-simplex honeycomb Coxeter, Regular and Semi-Regular Polytopes III, (1988), p318 Kaleidoscopes: Selected Writings of H. S. M. Coxeter
Quarter_5-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
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
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
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
D5 POLYTOPE
D5 POLYTOPE
D5 POLYTOPE
D5 POLYTOPE
Boy/Male
Arabic, Australian, Christian, Hindu, Indian, Muslim, Parsi, Pashtun, Tamil, Telugu
Knowledge; To be Clever; Wisdom; One who is Merciful and Foreseeing
Boy/Male
Gujarati, Hindu, Indian, Kannada, Telugu
Lord of the Heart; Beloved
Female
Finnish
 Finnish form of Low German Jannike, JANIKA means "God is gracious." Compare with another form of Janika.
Boy/Male
Hindu, Indian, Tamil, Thai
Older Brother
Girl/Female
Australian, Chinese
Precious
Girl/Female
Indian, Telugu
Peaceful
Male
French
French form of Latin Amadeus, AMADIEU means "to love God."
Girl/Female
Polish
Farmer.
Boy/Male
Hindu, Indian, Tamil
Lord Pandi Muni
Boy/Male
Hindu
Beautiful
D5 POLYTOPE
D5 POLYTOPE
D5 POLYTOPE
D5 POLYTOPE
D5 POLYTOPE