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Polytope constructed from alternation of a hypercube
In geometry, demihypercubes (also called n-demicubes, n-hemicubes, and half measure polytopes) are a class of n-polytopes constructed from alternation
Demihypercube
Polyhedron with four faces
parallel faces. Boerdijk–Coxeter helix Möbius configuration Caltrop Demihypercube and simplex – n-dimensional analogues Reeve tetrahedra Synergetics (Fuller)
Tetrahedron
Four-dimensional analog of the octahedron
the 16-cell, called a demitesseract or 4-demicube, a member of the demihypercube family, and represented by h{4,3,3}, and Coxeter diagrams or . It can
16-cell
Uniform 9-polytope
part of a dimensionally infinite family of uniform polytopes called demihypercubes. E. L. Elte identified it in 1912 as a semiregular polytope, labeling
9-demicube
Fundamental space of geometry
Polytopes and shapes Hyperplane Hypersurface Hypercube Hyperrectangle Demihypercube Hypersphere Cross-polytope Simplex Hyperpyramid Number systems Hypercomplex
Euclidean_space
Group of irregular uniform polytopes
the n-demihypercube as 1k1, and an alternated form of the n-orthoplex, k11, constructed with alternating simplex facets. Rectified n-demihypercubes, a lower
Gosset–Elte_figures
Regular 5-polytope
removed. It is a part of a dimensional family of uniform polytopes called demihypercubes for being alternation of the hypercube family. There are 23 uniform
5-demicube
Uniform 10-polytope
part of a dimensionally infinite family of uniform polytopes called demihypercubes. E. L. Elte identified it in 1912 as a semiregular polytope, labeling
10-demicube
Invariant measure of fractal dimension
Polytopes and shapes Hyperplane Hypersurface Hypercube Hyperrectangle Demihypercube Hypersphere Cross-polytope Simplex Hyperpyramid Number systems Hypercomplex
Hausdorff_dimension
Generalized sphere of dimension n (mathematics)
Polytopes and shapes Hyperplane Hypersurface Hypercube Hyperrectangle Demihypercube Hypersphere Cross-polytope Simplex Hyperpyramid Number systems Hypercomplex
N-sphere
Faster-than-light travel in science fiction
Polytopes and shapes Hyperplane Hypersurface Hypercube Hyperrectangle Demihypercube Hypersphere Cross-polytope Simplex Hyperpyramid Number systems Hypercomplex
Hyperspace
Uniform 6-polytope
part of a dimensionally infinite family of uniform polytopes called demihypercubes. Acronym: hax. E. L. Elte identified it in 1912 as a semiregular polytope
6-demicube
Uniform 8 dimensional polytope
part of a dimensionally infinite family of uniform polytopes called demihypercubes. E. L. Elte identified it in 1912 as a semiregular polytope, labeling
8-demicube
Number of vectors in any basis of the vector space
Polytopes and shapes Hyperplane Hypersurface Hypercube Hyperrectangle Demihypercube Hypersphere Cross-polytope Simplex Hyperpyramid Number systems Hypercomplex
Dimension_(vector_space)
Quasiregular space-filling tesselation
formed as an alternation of a hypercubic honeycomb and being composed of demihypercube and cross-polytope facets. It is also part of another infinite family
Tetrahedral-octahedral honeycomb
Tetrahedral-octahedral_honeycomb
Property of a mathematical space
Polytopes and shapes Hyperplane Hypersurface Hypercube Hyperrectangle Demihypercube Hypersphere Cross-polytope Simplex Hyperpyramid Number systems Hypercomplex
Dimension
Four-dimensional number system
Polytopes and shapes Hyperplane Hypersurface Hypercube Hyperrectangle Demihypercube Hypersphere Cross-polytope Simplex Hyperpyramid Number systems Hypercomplex
Quaternion
Convex polytope, the n-dimensional analogue of a square and a cube
Another related family of semiregular and uniform polytopes is the demihypercubes, which are constructed from hypercubes with alternate vertices deleted
Hypercube
Uniform 7-polytope
part of a dimensionally infinite family of uniform polytopes called demihypercubes. E. L. Elte identified it in 1912 as a semiregular polytope, labeling
7-demicube
Geometric space with five dimensions
Polytopes and shapes Hyperplane Hypersurface Hypercube Hyperrectangle Demihypercube Hypersphere Cross-polytope Simplex Hyperpyramid Number systems Hypercomplex
Five-dimensional_space
Manifold or algebraic variety of dimension n in a space of dimension n+1
Polytopes and shapes Hyperplane Hypersurface Hypercube Hyperrectangle Demihypercube Hypersphere Cross-polytope Simplex Hyperpyramid Number systems Hypercomplex
Hypersurface
Completion of the usual space with "points at infinity"
Polytopes and shapes Hyperplane Hypersurface Hypercube Hyperrectangle Demihypercube Hypersphere Cross-polytope Simplex Hyperpyramid Number systems Hypercomplex
Projective_space
Polygon with 2 sides and 2 vertices
topological structures, such as incidence structures. Monogon Polygon Demihypercube "ResearchGate". The Symmetries of Things 2008, John H. Conway, Heidi
Digon
Multi-dimensional generalization of triangle
Polytopes and shapes Hyperplane Hypersurface Hypercube Hyperrectangle Demihypercube Hypersphere Cross-polytope Simplex Hyperpyramid Number systems Hypercomplex
Simplex
Geometric model of the planar projection of the physical universe
Polytopes and shapes Hyperplane Hypersurface Hypercube Hyperrectangle Demihypercube Hypersphere Cross-polytope Simplex Hyperpyramid Number systems Hypercomplex
Euclidean_plane
In mathematics, a module that has a basis
Polytopes and shapes Hyperplane Hypersurface Hypercube Hyperrectangle Demihypercube Hypersphere Cross-polytope Simplex Hyperpyramid Number systems Hypercomplex
Free_module
Real-valued number of spatial dimensions
Polytopes and shapes Hyperplane Hypersurface Hypercube Hyperrectangle Demihypercube Hypersphere Cross-polytope Simplex Hyperpyramid Number systems Hypercomplex
Fractal_dimension
Invariant of topological spaces
Polytopes and shapes Hyperplane Hypersurface Hypercube Hyperrectangle Demihypercube Hypersphere Cross-polytope Simplex Hyperpyramid Number systems Hypercomplex
Inductive_dimension
In mathematics, dimension of a ring
Polytopes and shapes Hyperplane Hypersurface Hypercube Hyperrectangle Demihypercube Hypersphere Cross-polytope Simplex Hyperpyramid Number systems Hypercomplex
Krull_dimension
Type of uniform space-filling tessellation
of the regular 5-cube honeycomb. It is the first tessellation in the demihypercube honeycomb family which, with all the next ones, is not regular, being
5-demicubic_honeycomb
Method for producing composition algebras
Polytopes and shapes Hyperplane Hypersurface Hypercube Hyperrectangle Demihypercube Hypersphere Cross-polytope Simplex Hyperpyramid Number systems Hypercomplex
Cayley–Dickson_construction
Space with one dimension
Polytopes and shapes Hyperplane Hypersurface Hypercube Hyperrectangle Demihypercube Hypersphere Cross-polytope Simplex Hyperpyramid Number systems Hypercomplex
One-dimensional_space
Method of determining fractal dimension
Polytopes and shapes Hyperplane Hypersurface Hypercube Hyperrectangle Demihypercube Hypersphere Cross-polytope Simplex Hyperpyramid Number systems Hypercomplex
Minkowski–Bouligand_dimension
a coxeter diagram with ringed nodes representing active mirrors. A demihypercube is an alternation of a hypercube. Its 3-dimensional analogue would be
Cantic_7-cube
Number of independent parameters of a system
Polytopes and shapes Hyperplane Hypersurface Hypercube Hyperrectangle Demihypercube Hypersphere Cross-polytope Simplex Hyperpyramid Number systems Hypercomplex
Degrees_of_freedom
Family of regular tessellations in geometry
another mirror on an order-4 peak. The alternated hypercube facets become demihypercubes, and the deleted vertices create new orthoplex facets. The vertex figure
Alternated hypercubic honeycomb
Alternated_hypercubic_honeycomb
Mathematical space with two coordinates
Polytopes and shapes Hyperplane Hypersurface Hypercube Hyperrectangle Demihypercube Hypersphere Cross-polytope Simplex Hyperpyramid Number systems Hypercomplex
Two-dimensional_space
Geometric space with four dimensions
Polytopes and shapes Hyperplane Hypersurface Hypercube Hyperrectangle Demihypercube Hypersphere Cross-polytope Simplex Hyperpyramid Number systems Hypercomplex
Four-dimensional_space
Element of a unital algebra over the field of real numbers
Polytopes and shapes Hyperplane Hypersurface Hypercube Hyperrectangle Demihypercube Hypersphere Cross-polytope Simplex Hyperpyramid Number systems Hypercomplex
Hypercomplex_number
Geometric model of the physical space
Polytopes and shapes Hyperplane Hypersurface Hypercube Hyperrectangle Demihypercube Hypersphere Cross-polytope Simplex Hyperpyramid Number systems Hypercomplex
Three-dimensional_space
Mathematical model combining space and time
Polytopes and shapes Hyperplane Hypersurface Hypercube Hyperrectangle Demihypercube Hypersphere Cross-polytope Simplex Hyperpyramid Number systems Hypercomplex
Spacetime
Geometric space with eight dimensions
Polytopes and shapes Hyperplane Hypersurface Hypercube Hyperrectangle Demihypercube Hypersphere Cross-polytope Simplex Hyperpyramid Number systems Hypercomplex
Eight-dimensional_space
Matrix with one nonzero entry in each row and column
Coxeter group D n {\displaystyle D_{n}} and is the symmetry group of the demihypercube. It is a subgroup of the orthogonal group. Monomial matrices occur in
Generalized permutation matrix
Generalized_permutation_matrix
N-dimensional generalisation of a pyramid
Polytopes and shapes Hyperplane Hypersurface Hypercube Hyperrectangle Demihypercube Hypersphere Cross-polytope Simplex Hyperpyramid Number systems Hypercomplex
Hyperpyramid
Graph of the vertices and edges of a demihypercube
graph or half cube graph of dimension n is the vertex-edge graph of the demihypercube, formed by connecting pairs of vertices at distance exactly two from
Halved_cube_graph
Geometric space with seven dimensions
Polytopes and shapes Hyperplane Hypersurface Hypercube Hyperrectangle Demihypercube Hypersphere Cross-polytope Simplex Hyperpyramid Number systems Hypercomplex
Seven-dimensional_space
6-dimensional hypercube
uniform polytope, called a 6-demicube, (part of an infinite family called demihypercubes), which has 12 5-demicube and 32 5-simplex facets. This configuration
6-cube
Geometric object with flat sides
Polytopes and shapes Hyperplane Hypersurface Hypercube Hyperrectangle Demihypercube Hypersphere Cross-polytope Simplex Hyperpyramid Number systems Hypercomplex
Polytope
Fundamental object of geometry
Polytopes and shapes Hyperplane Hypersurface Hypercube Hyperrectangle Demihypercube Hypersphere Cross-polytope Simplex Hyperpyramid Number systems Hypercomplex
Point_(geometry)
Geometric space with six dimensions
Polytopes and shapes Hyperplane Hypersurface Hypercube Hyperrectangle Demihypercube Hypersphere Cross-polytope Simplex Hyperpyramid Number systems Hypercomplex
Six-dimensional_space
Surface in 3D space defined by an implicit function of three variables
Polytopes and shapes Hyperplane Hypersurface Hypercube Hyperrectangle Demihypercube Hypersphere Cross-polytope Simplex Hyperpyramid Number systems Hypercomplex
Implicit_surface
Hypercomplex number system
Polytopes and shapes Hyperplane Hypersurface Hypercube Hyperrectangle Demihypercube Hypersphere Cross-polytope Simplex Hyperpyramid Number systems Hypercomplex
Octonion
Mathematical transformation in physics
Polytopes and shapes Hyperplane Hypersurface Hypercube Hyperrectangle Demihypercube Hypersphere Cross-polytope Simplex Hyperpyramid Number systems Hypercomplex
Time-translation_symmetry
Mathematical coincidence
{\displaystyle \cong } A3 = D3 s l 4 ≅ s o 6 {\displaystyle {\mathfrak {sl}}_{4}\cong {\mathfrak {so}}_{6}} 3-simplex is 3-demihypercube (regular tetrahedron)
Exceptional_isomorphism
Geometric object
the beginning for completeness. The demipenteract also exists in the demihypercube family. They are also sometimes named by their symmetry group, like
Uniform_k_21_polytope
Topologically invariant definition of the dimension of a space
Polytopes and shapes Hyperplane Hypersurface Hypercube Hyperrectangle Demihypercube Hypersphere Cross-polytope Simplex Hyperpyramid Number systems Hypercomplex
Lebesgue_covering_dimension
Type of geometric object
{4,37} - 9-cube or enneract - {37,4} - 9-orthoplex or enneacross - Demihypercube D9 family: [36,1,1] - 383 uniform 9-polytope as permutations of rings
Uniform_9-polytope
7-dimensional hypercube
polytope, called a demihepteract, (part of an infinite family called demihypercubes), which has 14 demihexeractic and 64 6-simplex 6-faces. Coxeter, Regular
7-cube
8-dimensional hypercube
polytope, called an 8-demicube, (part of an infinite family called demihypercubes), which has 16 demihepteractic and 128 8-simplex facets. The 8-cube
8-cube
Geometric object used to describe rotation in any number of dimensions
Polytopes and shapes Hyperplane Hypersurface Hypercube Hyperrectangle Demihypercube Hypersphere Cross-polytope Simplex Hyperpyramid Number systems Hypercomplex
Plane_of_rotation
Subspace of n-space whose dimension is (n-1)
Polytopes and shapes Hyperplane Hypersurface Hypercube Hyperrectangle Demihypercube Hypersphere Cross-polytope Simplex Hyperpyramid Number systems Hypercomplex
Hyperplane
Hypercomplex number system
Polytopes and shapes Hyperplane Hypersurface Hypercube Hyperrectangle Demihypercube Hypersphere Cross-polytope Simplex Hyperpyramid Number systems Hypercomplex
Trigintaduonion
5-dimensional hypercube
called a 5-demicube, which is also part of an infinite family called the demihypercubes. The penteract can be seen as an order-3 tesseractic honeycomb on a
5-cube
Uniform 6-dimensional polytope
forms: {4,33} — 6-cube (hexeract) - {33,4} — 6-orthoplex, (hexacross) - Demihypercube D6 family: [33,1,1] - 47 uniform 6-polytopes (16 unique) as permutations
Uniform_6-polytope
as the halved cube graph and is the edge graphs of the corresponding demihypercube. The Turán graph T ( 2 n , n ) {\displaystyle T(2n,n)} (also known as
Graph_of_a_polytope
Property of a space in which the local dimensionality is the same everywhere
Polytopes and shapes Hyperplane Hypersurface Hypercube Hyperrectangle Demihypercube Hypersphere Cross-polytope Simplex Hyperpyramid Number systems Hypercomplex
Equidimensionality
Removal of alternate vertices
24-cell honeycomb. A hypercube can always be alternated into a uniform demihypercube. Cube → Tetrahedron (regular) → Tesseract (8-cell) → 16-cell (regular)
Alternation_(geometry)
Thing in mathematics and theoretical physics
Polytopes and shapes Hyperplane Hypersurface Hypercube Hyperrectangle Demihypercube Hypersphere Cross-polytope Simplex Hyperpyramid Number systems Hypercomplex
Quasi-sphere
regular polytopes Simplex Hypercube Cross-polytope Uniform polytope Demihypercube Uniform 1k2 polytope Uniform 2k1 polytope Uniform k21 polytope Honeycombs
List_of_mathematical_shapes
Generalization of a rectangle for higher dimensions
Polytopes and shapes Hyperplane Hypersurface Hypercube Hyperrectangle Demihypercube Hypersphere Cross-polytope Simplex Hyperpyramid Number systems Hypercomplex
Hyperrectangle
regular polytopes Simplex Hypercube Cross-polytope Uniform polytope Demihypercube Uniform 1k2 polytope Uniform 2k1 polytope Uniform k21 polytope Honeycombs
List of polygons, polyhedra and polytopes
List_of_polygons,_polyhedra_and_polytopes
9-dimensional hypercube
uniform polytope, called a 9-demicube, (part of an infinite family called demihypercubes), which has 18 8-demicube and 256 8-simplex facets. Klitzing, Richard
9-cube
7-demicube, a member of a dimensional family of uniform polytopes called demihypercubes for being alternation of the hypercube family. There are 95 uniform
Pentic_7-cubes
Topics referred to by the same term
graphics rendering Hemicube (geometry), an abstract regular polytope Demihypercube, an n-dimensional uniform polytope, also known as the n-hemicube This
Hemicube
10-dimensional hypercube
polytope, called a 10-demicube, (part of an infinite family called demihypercubes), which has 20 demienneractic and 512 enneazettonic facets. Klitzing
10-cube
1994 book by Michio Kaku
Polytopes and shapes Hyperplane Hypersurface Hypercube Hyperrectangle Demihypercube Hypersphere Cross-polytope Simplex Hyperpyramid Number systems Hypercomplex
Hyperspace_(book)
Polytope contained by 7-polytope facets
ones: {4,36} - 8-cube or octeract - {36,4} - 8-orthoplex or octacross - Demihypercube D8 family: [35,1,1] - 191 uniform 8-polytopes as permutations of rings
Uniform_8-polytope
Hypercomplex number system
Polytopes and shapes Hyperplane Hypersurface Hypercube Hyperrectangle Demihypercube Hypersphere Cross-polytope Simplex Hyperpyramid Number systems Hypercomplex
Sedenion
Measure of a mathematical object studied in the field of algebraic geometry
Polytopes and shapes Hyperplane Hypersurface Hypercube Hyperrectangle Demihypercube Hypersphere Cross-polytope Simplex Hyperpyramid Number systems Hypercomplex
Dimension of an algebraic variety
Dimension_of_an_algebraic_variety
Concept in geometry
5-demicube, a member of a dimensional family of uniform polytopes called demihypercubes for being alternation of the hypercube family. There are 23 uniform
Runcic_5-cubes
Five-dimensional geometric shape
5-polytopes Hypercube/Orthoplex family: B5 [4,33] 31 uniform 5-polytopes Demihypercube D5/E5 family: [32,1,1] 23 uniform 5-polytopes (8 unique) Polychoral
Uniform_5-polytope
Topological space of dimension zero
Polytopes and shapes Hyperplane Hypersurface Hypercube Hyperrectangle Demihypercube Hypersphere Cross-polytope Simplex Hyperpyramid Number systems Hypercomplex
Zero-dimensional_space
7-demicube, a member of a dimensional family of uniform polytopes called demihypercubes for being alternation of the hypercube family. There are 95 uniform
Runcic_7-cubes
Group of symmetries of an n-dimensional hypercube
{\displaystyle S_{n}^{\pm }} . It is also the symmetry group of the demihypercube, the polytope that one gets by taking the convex hull of every other
Hyperoctahedral_group
Regular polytope dual to the hypercube in any number of dimensions
Polytopes and shapes Hyperplane Hypersurface Hypercube Hyperrectangle Demihypercube Hypersphere Cross-polytope Simplex Hyperpyramid Number systems Hypercomplex
Cross-polytope
7-demicube, a member of a dimensional family of uniform polytopes called demihypercubes for being alternation of the hypercube family. There are 95 uniform
Hexic_7-cubes
Type of geometrical object
dekeract - {38,4} - 10-orthoplex or decacross - h{4,38} - 10-demicube - Demihypercube D10 family: [37,1,1] - 767 uniform 10-polytopes as permutations of rings
Uniform_10-polytope
5-demicube, a member of a dimensional family of uniform polytopes called demihypercubes for being alternation of the hypercube family. There are 23 uniform
Steric_5-cubes
Uniform 5-polytope
5-demicube, a part of a dimensional family of uniform polytopes called demihypercubes for being alternation of the hypercube family. There are 23 uniform
Cantic_5-cube
7-demicube, a member of a dimensional family of uniform polytopes called demihypercubes for being alternation of the hypercube family. There are 95 uniform
Steric_7-cubes
6-demicube, a part of a dimensional family of uniform polytopes called demihypercubes for being alternation of the hypercube family. There are 47 uniform
Runcic_6-cubes
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