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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
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
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 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
Geometric space with eight dimensions
Coxeter-Dynkin diagram. The 8-demicube is a unique polytope from the D8 family, and 421, 241, and 142 polytopes from the E8 family. The 7-sphere or hypersphere
Eight-dimensional_space
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
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
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
8-demicube facets around each vertex. 8-cubic honeycomb Uniform polytope "The Lattice D8". Sphere packings, lattices, and groups, by John Horton Conway
8-demicubic_honeycomb
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 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
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
Group of symmetries of the square
In mathematics, D4 (sometimes alternatively denoted by D8) is the dihedral group of degree 4 and order 8. It is the symmetry group of a square. As an example
Dihedral_group_of_order_8
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
Solid with eight equal triangular faces
segments. More generally, every cross-polytope and its dual, hypercube, in any higher-dimensional space are Hanner polytope. The polyhedral compounds, in which
Regular_octahedron
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
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
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
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
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
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
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
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
Any of the five regular polyhedra
are only three convex regular polytopes: the simplex as {3,3,...,3}, the hypercube as {4,3,...,3}, and the cross-polytope as {3,3,...,4}. In three dimensions
Platonic_solid
Polygon shape with eight sides
is the Petrie polygon for these higher-dimensional regular and uniform polytopes, shown in these skew orthogonal projections of in A7, B4, and D5 Coxeter
Octagon
Star polygon
of 5-cube and 5-orthoplex; that is, the compound of a n-cube and cross-polytope in their respective dual positions. An octagonal star can be seen as a
Octagram
7-homeycomb
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
7-simplex_honeycomb
Prism with an 8-sided base
uniform honeycombs: It is also an element of two four-dimensional uniform 4-polytopes: Weisstein, Eric W. "Octagonal prism". MathWorld. Interactive model of
Octagonal_prism
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
248-dimensional exceptional simple Lie group
are the vertices of a semi-regular polytope discovered by Thorold Gosset in 1900, sometimes known as the 421 polytope. In the so-called even coordinate
E8_(mathematics)
all trirectified 8-orthoplex facets and is the Voronoi tessellation of the D8* lattice. Facets can be identically colored from a doubled C ~ 8 {\displaystyle
8-cubic_honeycomb
Lattice in 8-dimensional space with special properties
simplices. The vertex figure of Gosset's honeycomb is the semiregular E8 polytope (421 in Coxeter's notation) given by the convex hull of the 240 roots of
E8_lattice
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
A000029 30-1 cases, skipping one with zero marks Norman Johnson Uniform Polytopes, Manuscript (1991) Kaleidoscopes: Selected Writings of H.S.M. Coxeter
Omnitruncated 7-simplex honeycomb
Omnitruncated_7-simplex_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
Polygon with 14 edges
skew tetradecagons exist as Petrie polygon for many higher-dimensional polytopes, shown in these skew orthogonal projections, including: Wantzel, Pierre
Tetradecagon
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
D8 POLYTOPE
D8 POLYTOPE
D8 POLYTOPE
D8 POLYTOPE
Girl/Female
Indian, Sanskrit
Moonlight; Moon's Rays
Male
Egyptian
, a VIth dynasty officer who was priest of Bast, &c.
Surname or Lastname
English (chiefly Devon)
English (chiefly Devon) : nickname for a thin or lean person, from Middle English lene ‘lean’ (Old English hlǣne).Irish : reduced Anglicized form of Gaelic Ó Liatháin (see Lehane).Reduced form of Scottish McLean.
Girl/Female
Indian
Preety
Girl/Female
Muslim
Girl/Female
Biblical
Agreeable, handsome.
Boy/Male
American, Anglo, Australian, British, Chinese, Christian, Dutch, English, French, German, Indian, Irish, Shakespearean, Tamil, Teutonic
Beacon Hill; Sword; Broom Covered Hill; Gorse Hill
Boy/Male
Hindu
Milk, Nectar
Boy/Male
Tamil
Suhastha | ஸà¯à®¹à®¾à®¸à¯à®¤à®¾
One of the kauravas
Boy/Male
Greek
Seer.
D8 POLYTOPE
D8 POLYTOPE
D8 POLYTOPE
D8 POLYTOPE
D8 POLYTOPE