AI & ChatGPT searches , social queries for 7 DEMICUBE
Search references for 7 DEMICUBE. Phrases containing 7 DEMICUBE
See searches and references containing 7 DEMICUBE!
Search references for 7 DEMICUBE. Phrases containing 7 DEMICUBE
See searches and references containing 7 DEMICUBE!7 DEMICUBE
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
Hexicated 7-simplex 7-demicube, Truncated 7-demicube, Cantellated 7-demicube, Runcinated 7-demicube, Stericated 7-demicube, Pentellated 7-demicube 7-cube,
List_of_mathematical_shapes
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 terated
Hexic_7-cubes
Hexicated 7-simplex 7-demicube, Truncated 7-demicube, Cantellated 7-demicube, Runcinated 7-demicube, Stericated 7-demicube, Pentellated 7-demicube 7-cube,
List of polygons, polyhedra and polytopes
List_of_polygons,_polyhedra_and_polytopes
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
geometry, 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
Steric_7-cubes
located in the 7-cube cell centers of the 8-cube. Rectified octeract Acronym: recto (Jonathan Bowers) Birectified octeract Rectified 8-demicube Acronym: bro
Rectified_8-cubes
runcinated 7-cube is a convex uniform 7-polytope with 3rd order truncations (runcination) of the regular 7-cube. There are 16 unique runcinations of the 7-cube
Runcinated_7-cubes
Polyhedron with four faces
and consecutive integers as edges, an example being the one with edges 6, 7, 8, 9, 10, and 11 and volume 48. The Royal Game of Ur, dating from 2600 BC
Tetrahedron
Uniform 9-polytope
In geometry, a demienneract or 9-demicube is a uniform 9-polytope, constructed from the 9-cube, with alternated vertices removed. It is part of a dimensionally
9-demicube
Geometric space with seven dimensions
Each uniform polytope is defined by a ringed Coxeter-Dynkin diagram. The 7-demicube is a unique polytope from the D7 family, and 321, 231, and 132 polytopes
Seven-dimensional_space
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, h3{4,35}, has
Runcic_7-cubes
Four-dimensional analogue of the cube
Polytopes (3rd ed.). Dover Publications. pp. 122–123. See the illustration Fig 7.2C. Hall, T. Proctor (1893). "The projection of fourfold figures on a three-flat"
Tesseract
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 cantic 7-cube or truncated 7-demicube as a uniform 7-polytope, being a truncation of the 7-demicube. A uniform 7-polytope is vertex-transitive
Cantic_7-cube
Uniform 10-polytope
In geometry, a 10-demicube or demidekeract is a uniform 10-polytope, constructed from the 10-cube with alternated vertices removed. It is part of a dimensionally
10-demicube
the 7-orthoplex, and 8-cube with 14 and 128 vertices respectively. The 7-demicube is added with half of the symmetry. They can be visualized as symmetric
B7_polytope
5-dimensional hypercube
vertices of the 5-cube, creates another uniform 5-polytope, called a 5-demicube, which is also part of an infinite family called the demihypercubes. The
5-cube
Polyhedron with 12 faces
{4}{3}}\cdot {\text{Long side}}} Short sides = 7 12 ⋅ Long side {\displaystyle {\text{Short sides}}={\sqrt {\frac {7}{12}}}\cdot {\text{Long side}}} The eight
Dodecahedron
Shape with six sides
5-cube 5-demicube Uniform 6-polytope 6-simplex 6-orthoplex • 6-cube 6-demicube 122 • 221 Uniform 7-polytope 7-simplex 7-orthoplex • 7-cube 7-demicube 132 •
Hexagon
Regular 5-polytope
In five-dimensional geometry, a demipenteract or 5-demicube is a semiregular 5-polytope, constructed from a 5-hypercube (penteract) with alternated vertices
5-demicube
Uniform polytope in 8 dimensional geometry
(triangles), 69,120 edges, and 2160 vertices. Its vertex figure is a 7-demicube. This polytope is a facet in the uniform tessellation, 251 with Coxeter-Dynkin
2_41_polytope
Uniform 7-Honeycomb
alternation of the regular 7-cubic honeycomb. It is composed of two different types of facets. The 7-cubes become alternated into 7-demicubes h{4,3,3,3,3,3} and
7-demicubic_honeycomb
Plane figure bounded by line segments
ISBN 0-415-15792-7. Mandik, Pete, Key Terms in Philosophy of Mind, Continuum International Publishing Group, 2010, p. 26, ISBN 1-84706-349-7. Kenny, Anthony
Polygon
Multi-dimensional generalization of triangle
by (1,1)n+1, like the coefficients of polynomial products. For example, a 7-simplex is (1,1)8 = (1,2,1)4 = (1,4,6,4,1)2 = (1,8,28,56,70,56,28,8,1). The
Simplex
6-cube, , has half of the vertices of a pentellated 6-cube, . Stericated 6-demicube Stericated demihexeract Small cellated hemihexeract (Acronym: sochax) (Jonathan
Pentic_6-cubes
Seven-dimensional geometric object
shared with C ~ 6 {\displaystyle {\tilde {C}}_{6}} , 32 new Uniform 6-demicube honeycomb, represented by symbols h{4,34,4} = {31,1,33,4}, = D ~ 6 {\displaystyle
Uniform_7-polytope
Shape with three equal sides
generates a sequence consisting of the first few numbers: 1, 1, 1, 2, 2, 3, 4, 5, 7, 9, 12, 16, 21, 28, ... (sequence A000931 in the OEIS) The Padovan sequence
Equilateral_triangle
7-dimensional hypercube
In geometry, a 7-cube is a seven-dimensional hypercube with 128 vertices, 448 edges, 672 square faces, 560 cubic cells, 280 tesseract 4-faces, 84 penteract
7-cube
Tessellation in Euclidean geometry
honeycomb, and a quarter of the vertices of a 7-cube honeycomb. Its facets are 7-demicubes, pentellated 7-demicubes, and {31,1,1}×{3,3} duoprisms. This honeycomb
Quarter_7-cubic_honeycomb
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
Type of 7-polytope
In 7-dimensional geometry, a 7-simplex is a self-dual regular 7-polytope. It has 8 vertices, 28 edges, 56 triangle faces, 70 tetrahedral cells, 56 5-cell
7-simplex
10-dimensional hypercube
vertices of the dekeract, creates another uniform polytope, called a 10-demicube, (part of an infinite family called demihypercubes), which has 20 demienneractic
10-cube
Uniform 6-polytope
In geometry, a 6-demicube, demihexeract or hemihexeract is a uniform 6-polytope, constructed from a 6-cube (hexeract) with alternated vertices removed
6-demicube
Solid with twenty equal triangular faces
≈ 5.196 {\displaystyle 3{\sqrt {3}}\approx 5.196} and 2 7 ≈ 5.292 {\displaystyle 2{\sqrt {7}}\approx 5.292} . The regular icosahedron has the thirty-one
Regular_icosahedron
Convex polytope, the n-dimensional analogue of a square and a cube
ISBN / Date incompatibility (help) Coxeter 1973, pp. 122–123, §7.2 see illustration Fig 7.2C. Miroslav Vořechovský; Jan Mašek; Jan Eliáš (November 2019)
Hypercube
5-cube 5-demicube Uniform 6-polytope 6-simplex 6-orthoplex • 6-cube 6-demicube 122 • 221 Uniform 7-polytope 7-simplex 7-orthoplex • 7-cube 7-demicube 132 •
E6_polytope
{\displaystyle \left(0,1,2,3,4\right)} The snub 5-demicube defined as an alternation of the omnitruncated 5-demicube is not uniform, but it can be given Coxeter
Runcinated_5-orthoplexes
Shape with five sides
5-cube 5-demicube Uniform 6-polytope 6-simplex 6-orthoplex • 6-cube 6-demicube 122 • 221 Uniform 7-polytope 7-simplex 7-orthoplex • 7-cube 7-demicube 132 •
Pentagon
seven-dimensional geometry, a runcinated 7-orthoplex is a convex uniform 7-polytope with 3rd order truncations (runcination) of the regular 7-orthoplex. There are 16 unique
Runcinated_7-orthoplexes
9-dimensional hypercube
another uniform polytope, called a 9-demicube, (part of an infinite family called demihypercubes), which has 18 8-demicube and 256 8-simplex facets. Klitzing
9-cube
Shape with four equal sides and angles
(PDF). Environment and Planning B: Planning and Design. 7 (2): 209–226. Bibcode:1980EnPlB...7..209S. doi:10.1068/b070209. Nakamura, Yuuka; Okazaki, Shigeyuki
Square
Equiangular and equilateral polygon
regular stars of up to 12 sides are: Pentagram – {5/2} Heptagram – {7/2} and {7/3} Octagram – {8/3} Enneagram – {9/2} and {9/4} Decagram – {10/3} Hendecagram
Regular_polygon
Uniform 8-polytope
geometry, a cantic 8-cube or truncated 8-demicube is a uniform 8-polytope, being a truncation of the 8-demicube. Truncated demiocteract Truncated hemiocteract;
Cantic_8-cube
7-simplex is a convex uniform 7-polytope with 4th order truncations (sterication) of the regular 7-simplex. There are 14 unique sterication for the 7-simplex
Stericated_7-simplexes
6-dimensional hypercube
another 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
shared with the B7 symmetry. There are two regular forms, the 7-orthoplex, and 7-demicube with 14 and 64 vertices respectively. They can be visualized
D7_polytope
Uniform 8 dimensional polytope
composed of 2400 facets: 240 132 polytopes, and 2160 7-demicubes (141). Its vertex figure is a birectified 7-simplex. This polytope, along with the demiocteract
1_42_polytope
Four-dimensional analog of the octahedron
There is a lower symmetry form of the 16-cell, called a demitesseract or 4-demicube, a member of the demihypercube family, and represented by h{4,3,3}, and
16-cell
Geometric object with flat sides
regular polytopes Opetope Polytope de Montréal Coxeter 1973, pp. 141–144, §7-x. Historical remarks. Coxeter (1973) Richeson, D. (2008). Euler's Gem: The
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 are 24 unique
Stericated_7-orthoplexes
Group of geometric symmetries with at least one fixed point
studying symmetries of molecules. They come in 7 infinite families of axial groups (also called prismatic), and 7 additional polyhedral groups (also called
Point_group
8-dimensional hypercube
vertices of the octeract, creates another uniform polytope, called an 8-demicube, (part of an infinite family called demihypercubes), which has 16 demihepteractic
8-cube
Polytope in 8-dimensional geometry
ringed node and adding rings to the neighboring nodes. This makes a 5-demicube-triangular duoprism. These graphs represent orthographic projections in
4_21_polytope
Convex regular polytope in 10 dimensional geometry
tetrahedron cells, 8064 5-cell 4-faces, 13440 5-faces, 15360 6-faces, 11520 7-faces, 5120 8-faces, and 1024 9-faces. It has two constructed forms, the first
10-orthoplex
Solid with eight equal triangular faces
between a triangle and a square is arctan ( 2 ) ≈ 54.7 ∘ {\displaystyle \arctan({\sqrt {2}})\approx 54.7^{\circ }} . Therefore, for the regular octahedron
Regular_octahedron
7-simplex is a convex uniform 7-polytope with 3rd order truncations (runcination) of the regular 7-simplex. There are 8 unique runcinations of the 7-simplex
Runcinated_7-simplexes
5-dimensional geometric object
5-simplex honeycomb, . The 5-demicube honeycomb, , vertex figure is a rectified 5-orthoplex and facets are the 5-orthoplex and 5-demicube. Pyramidal 5-polytopes
5-polytope
unique 4 steric forms of the 6-cube. Runcinated demihexeract Runcinated 6-demicube Small prismated hemihexeract (Acronym: sophax) (Jonathan Bowers) The Cartesian
Steric_6-cubes
Regular Schläfli-Hess 4-polytope with 600 vertices
5-cube 5-demicube Uniform 6-polytope 6-simplex 6-orthoplex • 6-cube 6-demicube 122 • 221 Uniform 7-polytope 7-simplex 7-orthoplex • 7-cube 7-demicube 132 •
Great grand stellated 120-cell
Great_grand_stellated_120-cell
5-cube 5-demicube Uniform 6-polytope 6-simplex 6-orthoplex • 6-cube 6-demicube 122 • 221 Uniform 7-polytope 7-simplex 7-orthoplex • 7-cube 7-demicube 132 •
Runcinated_tesseracts
Uniform 7- polytope
7-cube is a convex uniform 7-polytope, being a truncation of the regular 7-cube. There are 6 truncations for the 7-cube. Vertices of the truncated 7-cube
Truncated_7-cubes
Uniform 6-polytope
self-dual regular 6-polytope. It has 7 vertices, 21 edges, 35 triangle faces, 35 tetrahedral cells, 21 5-cell 4-faces, and 7 5-simplex 5-faces. Its dihedral
6-simplex
Convex regular 8-polytope
126 5-cell 4-faces, 84 5-simplex 5-faces, 36 6-simplex 6-faces, and 9 7-simplex 7-faces. Its dihedral angle is cos−1(1/8), or approximately 82.82°. It
8-simplex
Convex uniform 7-polytope
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
similarly to the monogon and digon, may exist (for example: {3/2}, {5/3}, {5/4}, {7/4}, {9/5}), however these have not been studied in detail. There also exist
List_of_regular_polytopes
geometry, a pentellated 7-orthoplex is a convex uniform 7-polytope with 5th order truncations (pentellation) of the regular 7-orthoplex. There are 32
Pentellated_7-orthoplexes
Regular object in four dimensional geometry
includes [ 4 ] R − q 7 , − q 8 {\displaystyle [4]R_{-q7,-q8}} , [ 4 ] R q 8 , q 7 {\displaystyle [4]R_{q8,q7}} and [ 4 ] R − q 8 , − q 7 {\displaystyle [4]R_{-q8
24-cell
Four-dimensional geometric objects
5-cube 5-demicube Uniform 6-polytope 6-simplex 6-orthoplex • 6-cube 6-demicube 122 • 221 Uniform 7-polytope 7-simplex 7-orthoplex • 7-cube 7-demicube 132 •
H4_polytope
7-polytope
a truncated 7-orthoplex is a convex uniform 7-polytope, being a truncation of the regular 7-orthoplex. There are 6 truncations of the 7-orthoplex. Vertices
Truncated_7-orthoplexes
uniform 6-polytope. There are 2 unique runcic for the 6-cube. Cantellated 6-demicube Cantellated demihexeract Small rhombated hemihexeract (Acronym: sirhax)
Runcic_6-cubes
5-cube 5-demicube Uniform 6-polytope 6-simplex 6-orthoplex • 6-cube 6-demicube 122 • 221 Uniform 7-polytope 7-simplex 7-orthoplex • 7-cube 7-demicube 132 •
E8_polytope
Uniform 5-polytope
cantic 5-cube, cantihalf 5-cube, truncated 5-demicube is a uniform 5-polytope, being a truncation of the 5-demicube. It has half the vertices of a cantellated
Cantic_5-cube
Uniform 4-polytope
5-cube 5-demicube Uniform 6-polytope 6-simplex 6-orthoplex • 6-cube 6-demicube 122 • 221 Uniform 7-polytope 7-simplex 7-orthoplex • 7-cube 7-demicube 132 •
Truncated_120-cells
Regular 5-polytope
5-cube 5-demicube Uniform 6-polytope 6-simplex 6-orthoplex • 6-cube 6-demicube 122 • 221 Uniform 7-polytope 7-simplex 7-orthoplex • 7-cube 7-demicube 132 •
5-simplex
7-orthoplex. The rectified 6-simplex polytope is the vertex figure of the 7-demicube, and the edge figure of the uniform 241 polytope. These polytopes are
Rectified_6-simplexes
5-cube 5-demicube Uniform 6-polytope 6-simplex 6-orthoplex • 6-cube 6-demicube 122 • 221 Uniform 7-polytope 7-simplex 7-orthoplex • 7-cube 7-demicube 132 •
Cantellated_5-simplexes
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
most simply positioned in 7-space as permutations of (0,0,0,0,0,1,2). This construction is based on facets of the truncated 7-orthoplex. Bitruncated heptapeton
Truncated_6-simplexes
Type of geometric object
as permutations of rings in the group diagram, including: {31,6,1} - 9-demicube or demienneract, 161 - ; also as h{4,38} - {36,1,1} - 9-orthoplex, 611
Uniform_9-polytope
5-cube 5-demicube Uniform 6-polytope 6-simplex 6-orthoplex • 6-cube 6-demicube 122 • 221 Uniform 7-polytope 7-simplex 7-orthoplex • 7-cube 7-demicube 132 •
Rectified_9-cubes
cantellated 7-cube is a convex uniform 7-polytope, being a cantellation of the regular 7-cube. There are 10 degrees of cantellation for the 7-cube, including
Cantellated_7-cubes
cantellated 7-orthoplex is a convex uniform 7-polytope, being a cantellation of the regular 7-orthoplex. There are ten degrees of cantellation for the 7-orthoplex
Cantellated_7-orthoplexes
Four-dimensional analogue of the tetrahedron
Johnson 2018, p. 249. Ghyka 1977, p. 68. Coxeter 1973, p. 120, §7.2. see illustration Fig 7.2A. Miyazaki & Ishii 2021, p. 46. Diudea 2018, p. 41. Akiyama
5-cell
Uniform Polytope
6-demicube. Its 126 vertices represent the root vectors of the simple Lie group E7. This polytope is the vertex figure for a uniform tessellation of 7-dimensional
2_31_polytope
Type of tesseract
5-cube 5-demicube Uniform 6-polytope 6-simplex 6-orthoplex • 6-cube 6-demicube 122 • 221 Uniform 7-polytope 7-simplex 7-orthoplex • 7-cube 7-demicube 132 •
Truncated_tesseract
pentellated 7-cube is a convex uniform 7-polytope with 5th order truncations (pentellation) of the regular 7-cube. There are 32 unique pentellations of the 7-cube
Pentellated_7-cubes
Uniform 6-polytope
facets: 27 5-orthoplexes and 72 5-simplices. Its vertex figure is a 5-demicube. For visualization this 6-dimensional polytope is often displayed in a
2_21_polytope
5-cube 5-demicube Uniform 6-polytope 6-simplex 6-orthoplex • 6-cube 6-demicube 122 • 221 Uniform 7-polytope 7-simplex 7-orthoplex • 7-cube 7-demicube 132 •
Stericated_5-cubes
Uniform polytope
5-demicube (demipenteract) in 5 dimensions, and the 4-simplex (5-cell) in 4 dimensions. Each polytope is constructed from 1k−1,2 and (n−1)-demicube facets
Uniform_1_k2_polytope
Polytope with highest degree of symmetry
that are impossible to construct are the n-sided polygons with n equal to 7, 9, 11, 13, 14, 18, 19, 21,... Constructibility in this sense refers only
Regular_polytope
Concept in geometry
In five-dimensional geometry, a runcic 5-cube, runcic 5-demicube or runcihalf 5-cube, is a convex uniform 5-polytope. There are 2 runcic forms for the
Runcic_5-cubes
Four-dimensional geometrical object
5-cube 5-demicube Uniform 6-polytope 6-simplex 6-orthoplex • 6-cube 6-demicube 122 • 221 Uniform 7-polytope 7-simplex 7-orthoplex • 7-cube 7-demicube 132 •
Runcinated_5-cell
Four-dimensional analog of the dodecahedron
8 vertices of the 4-orthoplex. Uniquely, the 4-orthoplex is also the 4-demicube, half the vertices of the 4-cube. This relationship among the 4-simplex
120-cell
the 10-simplex. The rectified 10-simplex is the vertex figure of the 11-demicube. Rectified hendecaxennon (acronym: ru) (Jonathan Bowers) The Cartesian
Rectified_10-simplexes
Convex uniform 7-polytope in seven-dimensional geometry
seven-dimensional geometry, a rectified 7-simplex is a convex uniform 7-polytope, being a rectification of the regular 7-simplex. There are four unique degrees
Rectified_7-simplexes
polychora based on the icositetrachoron (24-cell) - Model 23, George Olshevsky. 7. Uniform polychora derived from glomeric tetrahedron B4 - Model 23, George
Rectified_24-cell
cantellated 7-simplex is a convex uniform 7-polytope, being a cantellation of the regular 7-simplex. There are unique 6 degrees of cantellation for the 7-simplex
Cantellated_7-simplexes
5-cube 5-demicube Uniform 6-polytope 6-simplex 6-orthoplex • 6-cube 6-demicube 122 • 221 Uniform 7-polytope 7-simplex 7-orthoplex • 7-cube 7-demicube 132 •
B4_polytope
Regular polytope whose 2D form is a pentagon
5-cube 5-demicube Uniform 6-polytope 6-simplex 6-orthoplex • 6-cube 6-demicube 122 • 221 Uniform 7-polytope 7-simplex 7-orthoplex • 7-cube 7-demicube 132 •
Pentagonal_polytope
7 DEMICUBE
7 DEMICUBE
7 DEMICUBE
7 DEMICUBE
7 DEMICUBE
7 DEMICUBE
7 DEMICUBE
7 DEMICUBE
7 DEMICUBE