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geometry, a rectified 9-cube is a convex uniform 9-polytope, being a rectification of the regular 9-cube. There are 9 rectifications of the 9-cube. The zeroth
Rectified_9-cubes
birectified 5-cube are located in the square face centers of the 5-cube. Rectified penteract (acronym: rin) (Jonathan Bowers) The rectified 5-cube may be constructed
Rectified_5-cubes
centers of the 7-cube. rectified hepteract (acronym: rasa) (Jonathan Bowers) Cartesian coordinates for the vertices of a rectified 7-cube, centered at the origin
Rectified_7-cubes
geometry, a rectified 10-cube is a convex uniform 10-polytope, being a rectification of the regular 10-cube. There are 10 rectifications of the 10-cube, with
Rectified_10-cubes
geometry, a rectified 9-simplex is a convex uniform 9-polytope, being a rectification of the regular 9-orthoplex. There are 9 rectifications of the 9-orthoplex
Rectified_9-orthoplexes
7-cube cell centers of the 8-cube. Rectified octeract Acronym: recto (Jonathan Bowers) Birectified octeract Rectified 8-demicube Acronym: bro (Jonathan
Rectified_8-cubes
Geometrical Shape
birectified 6-cube are located in the square face centers of the 6-cube. Rectified hexeract (acronym: rax) (Jonathan Bowers) The rectified 6-cube may be constructed
Rectified_6-cubes
rectified 24-cell or rectified icositetrachoron is a uniform 4-dimensional polytope (or uniform 4-polytope), which is bounded by 48 cells: 24 cubes,
Rectified_24-cell
Polyhedron with 8 triangles and 6 squares
A cuboctahedron, rectified cube, or rectified octahedron is a polyhedron with 8 triangular faces and 6 square faces. A cuboctahedron has 12 identical vertices
Cuboctahedron
Type of geometric object
regular 9-polytopes: {3,3,3,3,3,3,3,3} - 9-simplex {4,3,3,3,3,3,3,3} - 9-cube {3,3,3,3,3,3,3,4} - 9-orthoplex There are no nonconvex regular 9-polytopes
Uniform_9-polytope
5-demicube 5-cube, Rectified 5-cube, 5-cube, Truncated 5-cube, Cantellated 5-cube, Runcinated 5-cube, Stericated 5-cube 5-orthoplex, Rectified 5-orthoplex
List_of_mathematical_shapes
6-demicube 6-cube, Rectified 6-cube, Truncated 6-cube, Cantellated 6-cube, Runcinated 6-cube, Stericated 6-cube, Pentellated 6-cube 6-orthoplex, Rectified 6-orthoplex
List of polygons, polyhedra and polytopes
List_of_polygons,_polyhedra_and_polytopes
Only regular space-filling tessellation of the cube
honeycomb) in Euclidean 3-space made up of cubic cells. It has 4 cubes around every edge, and 8 cubes around each vertex. Its vertex figure is a regular octahedron
Cubic_honeycomb
In geometry, the rectified tesseract, rectified 8-cell is a uniform 4-polytope (4-dimensional polytope) bounded by 24 cells: 8 cuboctahedra, and 16 tetrahedra
Rectified_tesseract
Polytope in 8-dimensional geometry
orthoplexes. The rectified 421 can be seen as a rectification of the 421 polytope, creating new vertices on the center of edges of the 421. Rectified
4_21_polytope
Type of geometric object
of the 10-demicube. Rectified decayotton (reday) (Jonathan Bowers) The Cartesian coordinates of the vertices of the rectified 9-simplex can be most simply
Rectified_9-simplexes
Polyhedron with eight triangular faces
vertices at which four sides meet, and twelve edges. Its dual polyhedron is a cube. It can be formed as the convex hull of the six axis-parallel unit vectors
Octahedron
semiregular polytope, labeling it as S1 5. Rectified hexateron (Acronym: rix) (Jonathan Bowers) The vertices of the rectified 5-simplex can be more simply positioned
Rectified_5-simplexes
constructed from this honeycomb. or rectified heptacross rectified hecatonicosaoctaexon (Acronym: rez) (Jonathan Bowers) - rectified 128-faceted polyexon There
Rectified_7-orthoplexes
Uniform 6-dimensional polytope
uniform polypeta are regular polypeta: the 6-simplex {3,3,3,3,3}, the 6-cube (hexeract) {4,3,3,3,3}, and the 6-orthoplex (hexacross) {3,3,3,3,4}. Regular
Uniform_6-polytope
the 6-orthoplex. The rectified 6-orthoplex is the vertex figure for the demihexeractic honeycomb. or Rectified hexacross Rectified hexacontatetrapeton
Rectified_6-orthoplexes
as a first rectification of a 5-dimensional cross polytope. Rectified pentacross Rectified triacontaditeron (32-faceted 5-polytope) Acronym: rat (Jonathan
Rectified_5-orthoplexes
13k series. The final is a noncompact hyperbolic honeycomb, 134. The rectified 133 or 0331, Coxeter diagram has facets and , and vertex figure .
1_33_honeycomb
Tiling of hyperbolic 3-space by uniform polyhedra
made from 8 cubes and 12 p-gonal prisms at a vertex for any integer p. In the case p = 4 (a regular icosahedron), all cells are cubes and the result
Uniform honeycombs in hyperbolic space
Uniform_honeycombs_in_hyperbolic_space
Uniform 6-polytope
(dual of E6 lattice). Birectified 221 polytope Rectified pentacontatetrapeton (Acronym: ram) - rectified 54-facetted polypeton (Jonathan Bowers) Vertices
1_22_polytope
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
of tetrahedron and icosahedron cells. (The other two are the rectified 5-cell and rectified 600-cell.) Snub icositetrachoron Snub demitesseract Semi-snub
Snub_24-cell
Archimedean solid with 26 faces
constructed from a cube by drawing a smaller one in the middle of each face, parallel to the cube's edges. After removing the edges of a cube, the squares may
Rhombicuboctahedron
Polytope constructed from alternation of a hypercube
the vertices of {4,3,...,3}. The vertex figures of demihypercubes are rectified n-simplexes. They are represented by Coxeter-Dynkin diagrams of three
Demihypercube
Convex uniform 7-polytope in seven-dimensional geometry
semiregular polytope, labeling it as S1 7. Rectified octaexon (Acronym: roc) (Jonathan Bowers) The vertices of the rectified 7-simplex can be most simply positioned
Rectified_7-simplexes
Type of tesseract
envelope is a cube. Two of the truncated cube cells project onto a truncated cube inscribed in the cubical envelope. The other 6 truncated cubes project onto
Truncated_tesseract
Uniform Polytope
group orders. The rectified 231 is a rectification of the 231 polytope, creating new vertices on the center of edge of the 231. Rectified
2_31_polytope
Seven-dimensional geometric object
convex regular 7-polytopes: {3,3,3,3,3,3} - 7-simplex {4,3,3,3,3,3} - 7-cube {3,3,3,3,3,4} - 7-orthoplex There are no nonconvex regular 7-polytopes. The
Uniform_7-polytope
Type of geometrical object
with one or more rings. Twelve cases are shown below: ten single-ring (rectified) forms, and two truncations. Bowers-style acronym names are given in parentheses
Uniform_10-polytope
Class of 4-dimensional polytopes
Space of n Dimensions. In four dimensions, this gives the rectified 5-cell, the rectified 600-cell, and the snub 24-cell. 1910: Alicia Boole Stott, in
Uniform_4-polytope
is cell-transitive, consisting of 48 truncated cubes, and also edge-transitive, with 3 truncated cubes cells per edge and with one triangle and two octagons
Truncated_24-cells
Uniform 6-polytope
in dimensional series 22k. The rectified 221 has 216 vertices, and 126 facets: 72 rectified 5-simplices, and 27 rectified 5-orthoplexes and 27 5-demicubes
2_21_polytope
Uniform polychoron
(Thorold Gosset) Dispentachoron Rectified 5-cell (Norman W. Johnson) Rectified 4-simplex Fully truncated 4-simplex Rectified pentachoron (Acronym: rap) (Jonathan
Rectified_5-cell
Natural number
regular compounds. The cuboctahedron, on the other hand, is a rectified cube or rectified octahedron, and one of only two convex quasiregular polyhedra
8
Uniform polytope
triangle, doubled into a prism: {3,3}×{3}×{}. Rectified pentacontahexa-hecatonicosihexa-exon for rectified 56-126 facetted polyexon (acronym: lanq) (Jonathan
1_32_polytope
Uniform 7-dimensional polytope
3-sphere tiling, a tetrahedral hosohedron.) Rectified hecatonicosihexa-pentacosiheptacontahexa-exon as a rectified 126-576 facetted polyexon (acronym: ranq)
3_21_polytope
In geometry, the rectified 600-cell or rectified hexacosichoron is a convex uniform 4-polytope composed of 600 regular octahedra and 120 icosahedra cells
Rectified_600-cell
Group of irregular uniform polytopes
and all rectified (single-ring) Coxeter–Dynkin diagrams. The family of n-simplices contain Gosset–Elte figures of the form 0ij as all rectified forms of
Gosset–Elte_figures
Uniform 8-polytope
In 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
Cantic_8-cube
Convex uniform 4-polytope
eight cubes becomes a rhombicuboctahedron in the described way. In addition however, since each cube's edge was previously shared with two other cubes, the
Cantellated_tesseract
Geometric space with five dimensions
kissing number of the lattice, 30, is represented in its vertices. The rectified 5-orthoplex is the vertex figure of the D5 lattice, . Its 40 vertices
Five-dimensional_space
disprismatotesseractihexadecachoron has 16 tetrahedra, 32 cubes, and 32 triangular prisms. Each vertex is shared by 4 cubes, 3 triangular prisms and one tetrahedron.
Runcinated_tesseracts
Uniform 8 dimensional polytope
polytope Quadrirectified 421 polytope Rectified diacositetraconta-dischiliahectohexaconta-zetton as a rectified 240-2160 facetted polyzetton (acronym:
1_42_polytope
Regular 5-polytope
called the Clebsch graph, though that name sometimes refers to the folded cube graph of order five instead. Cartesian coordinates for the vertices of a
5-demicube
Uniform polytope in 8 dimensional geometry
also shown. The rectified 241 is a rectification of the 241 polytope, with vertices positioned at the mid-edges of the 241. Rectified
2_41_polytope
symmetry, and E6 has 12 symmetry. Six symmetry planes graphs are shown for 9 of the 39 polytopes in the E6 symmetry. The vertices and edges drawn with
E6_polytope
In eight-dimensional geometry, a rectified 8-simplex is a convex uniform 8-polytope, being a rectification of the regular 8-simplex. There are unique
Rectified_8-simplexes
Archimedean solid with 32 faces
contributing two radii and an edge. The icosidodecahedron is a rectified dodecahedron and also a rectified icosahedron, existing as the full-edge truncation between
Icosidodecahedron
cube (), and octahedron (). The Hessian is analogous to the tetrahedron, like the cube is a double tetrahedron, and the octahedron as a rectified tetrahedron
Hessian_polyhedron
Type of uniform space-filling tessellation
densest known sphere packing in 5 dimensions. The 40 vertices of the rectified 5-orthoplex vertex figure of the 5-demicubic honeycomb reflect the kissing
5-demicubic_honeycomb
Isogonal polytope with uniform facets
and so on. An extended Schläfli symbol can be used for representing rectified forms, with a single subscript: k-th rectification = tk{p1, p2, ..., pn−1}
Uniform_polytope
[8] 1 421 (fy) 2 Rectified 421 (riffy) 3 Birectified 421 (borfy) 4 Trirectified 421 (torfy) 5 Rectified 142 (buffy) 6 Rectified 241 (robay) 7 241 (bay)
E8_polytope
Isogonal polyhedron with regular faces
which can be split as a union of polyhedra, such as the compound of 5 cubes. If we drop the condition that the realization of the polyhedron is non-degenerate
Uniform_polyhedron
In 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
Cantic_7-cube
Polyhedron made by truncating one end of a trapezohedron
faces. It can also be seen as a tetrahedron with 3 of 4 of its vertices rectified. The three rhombic faces fold out flat to form half of a hexagram. Elongated
Diminished_trapezohedron
5-cell centers of the 10-simplex. The rectified 10-simplex is the vertex figure of the 11-demicube. Rectified hendecaxennon (acronym: ru) (Jonathan Bowers)
Rectified_10-simplexes
forms, the 5-orthoplex, and 5-cube with 10 and 32 vertices respectively. The 5-demicube is added as an alternation of the 5-cube. They can be visualized as
B5_polytope
simple Lie groups. The rectified 8-orthoplex is the vertex figure for the demiocteractic honeycomb. or Rectified octacross Rectified diacosipentacontahexazetton
Rectified_8-orthoplexes
Five-dimensional geometric shape
such regular polytopes, all convex: {3,3,3,3} - 5-simplex {4,3,3,3} - 5-cube {3,3,3,4} - 5-orthoplex There are no nonconvex regular polytopes in 5 dimensions
Uniform_5-polytope
the square faces. The 24-cell facets exist between these vertices as rectified 16-cells. If the coordinates of the tesseractic honeycomb are integers
24-cell_honeycomb
Convex polyhedron whose faces are almost regular polygons
Truncated tetrahedron Truncated octahedron 4.4.4.4 Square icositetrahedron (Cube) 3.4.6.4: Hexagonal cupola (Degenerate) Geodesic polyhedron Goldberg polyhedron
Near-miss_Johnson_solid
A3 [4] Cube centered Tetrahedron centered 13 *rectified 16-cell (Same as 24-cell) = r{3,3,4} = {3,4,3} 14 *cantellated 16-cell (Same as rectified 24-cell)
B4_polytope
Geometric operation applied to a polyhedron
, r } {\displaystyle s{\begin{Bmatrix}p,q,r\end{Bmatrix}}} , and . A rectified polychoron { p q , r } {\displaystyle {\begin{Bmatrix}p\\q,r\end{Bmatrix}}}
Snub_(geometry)
Tessellation of convex uniform polyhedron cells
9 forms, generated by ring permutations of the Coxeter group: . There are 9 forms, generated by ring permutations of the Coxeter group: There are 9 forms
Paracompact uniform honeycombs
Paracompact_uniform_honeycombs
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
Uniform 10-polytope
10-demicube or demidekeract is a uniform 10-polytope, constructed from the 10-cube with alternated vertices removed. It is part of a dimensionally infinite
10-demicube
Uniform 4-polytope
120-cell Truncated 120-cell Rectified 120-cell Bitruncated 120-cell Bitruncated 600-cell 600-cell Truncated 600-cell Rectified 600-cell Orthogonal projections
Truncated_120-cells
Geometric object
) The family starts uniquely as 6-polytopes. The triangular prism and rectified 5-cell are included at the beginning for completeness. The demipenteract
Uniform_k_21_polytope
Coxeter-Dynkin diagram, shown as . Rectified heptapeton (Acronym: ril) (Jonathan Bowers) The vertices of the rectified 6-simplex can be most simply positioned
Rectified_6-simplexes
Concept in euclidean geometry
centered cubic (a checkerboard in which the red 4-cubes have a central vertex but the black 4-cubes do not). The tesseract can make a regular tessellation
Tesseractic_honeycomb
Regular object in four dimensional geometry
polytopes constructed from the 24-cell. The 24-cell can also be derived as a rectified 16-cell: Octacube (sculpture) Uniform 4-polytope § The F4 family Coxeter
24-cell
In 4-dimensional geometry, there are 9 uniform 4-polytopes with F4 symmetry, and one chiral half symmetry, the snub 24-cell. There is one self-dual regular
List_of_F4_polytopes
Four-dimensional geometric objects
Dodecahedron centered Tetrahedron centered 1 120-cell {5,3,3} 2 rectified 120-cell r{5,3,3} 3 rectified 600-cell r{3,3,5} 4 600-cell {3,3,5} 5 truncated 120-cell
H4_polytope
Parallel 3D Net F4 [12] B4 [8] D4, B3 [6] D3, B2 [2] Cube centered Tetrahedron centered D4 [6] 5 rectified 16-cell (Same as 24-cell) = = {31,1,1} = r{3,3,4}
D4_polytope
Polytope contained by 7-polytope facets
convex regular 8-polytopes: {3,3,3,3,3,3,3} - 8-simplex {4,3,3,3,3,3,3} - 8-cube {3,3,3,3,3,3,4} - 8-orthoplex There are no nonconvex regular 8-polytopes
Uniform_8-polytope
In 4-dimensional geometry, there are 9 uniform polytopes with A4 symmetry. There is one self-dual regular form, the 5-cell with 5 vertices. A4 symmetry
A4_polytope
6-dimensional geometric object
6-simplex honeycomb, . The 6-demicube honeycomb, , vertex figure is a rectified 6-orthoplex and facets are the 6-orthoplex and 6-demicube. The uniform
6-polytope
4D geometry item
Cantellated tetrahedron (Cuboctahedron) 1 1200 None (Degenerate triangular prism) 2 720 Pentagonal prism 3 120 Rectified dodecahedron (Icosidodecahedron)
Cantellated_120-cell
Natural mineral form of lead sulfide
radio receivers, in which it was used as a point-contact diode capable of rectifying alternating current to detect the radio signals. The galena crystal was
Galena
Dutch artist
Martens". CTC-CTI. Retrieved 2022-07-06. Renzo Martens - Plantations and White Cubes, Goldsmiths College Department of Art MFA Lectures 2018 - 2019, retrieved
Renzo_Martens
Group of polytopes
with half symmetry). There are two regular forms, the 8-orthoplex and 8-cube, with 16 and 256 vertices respectively. They can be visualized as symmetric
B8_polytope
Type of uniform 4-polytope in four-dimensional geography
prismatic prism - - 4 cubes and 4 cubes - (same as 4-4 duoprism and same as tesseract) Pentagonal prismatic prism - - 5 cubes and 4 pentagonal prisms
Prismatic_uniform_4-polytope
Uniform 8 dimensional polytope
vertices of an 8-demicube centered at the origin are alternate halves of the 8-cube: (±1,±1,±1,±1,±1,±1,±1,±1) with an odd number of plus signs. This polytope
8-demicube
24-cell honeycomb, containing tesseract and rectified 24-cell cells. Rectified icositetrachoric tetracomb Rectified icositetrachoric honeycomb Cantellated
Rectified_24-cell_honeycomb
Sweetened, anise-flavored Turkish alcoholic drink
that is distilled to a maximum of 94.55% abv. This spirit is not highly rectified spirit and unlike other flavoured spirits Raki producers consider that
Rakı
8-cubic honeycomb. It is composed of two different types of facets. The 8-cubes become alternated into 8-demicubes h{4,3,3,3,3,3,3} and the alternated vertices
8-demicubic_honeycomb
120-cell was built by a team led by Daniel Duddy and David Richter on August 9, 2006 using the Zome system in the London Knowledge Lab for the 2006 Bridges
Runcinated_120-cells
2001 basketball video game
Concepts and published by Sega for Dreamcast, PlayStation 2, Xbox and GameCube. NBA 2K2 featured more street courts such as Mosswood, Fonde Rec Center,
NBA_2K2
2 Rectified 231 (rolaq) 3 Rectified 132 (rolin) 4 132 (lin) 5 Birectified 321 (branq) 6 Rectified 321 (ranq) 7 321 (naq) 8 Truncated 231 (talq) 9 Truncated
E7_polytope
Dutch mathematician (1881–1943)
Polyhedra: Regular: T, C, O, I, D Truncated: tT, tC, tO, tI, tD Quasiregular (rectified): CO, ID Cantellated: RCO, RID Truncated quasiregular (omnitruncated):
Emanuel_Lodewijk_Elte
Indian marketing manager
the idea on Manjunath's 10th death anniversary. They used 23,278 Rubik's cubes to build the mosaic representing Manjunath's birthday (23 February 1978)
Shanmugam_Manjunath
Self-intersecting uniform polyhedron
cubes sharing edges and vertices) Great complex rhombicosidodecahedron (looks like a great ditrigonal icosidodecahedron and a compound of five cubes sharing
Uniform_star_polyhedron
polytopes with B7 symmetry. There are two regular forms, the 7-orthoplex, and 8-cube with 14 and 128 vertices respectively. The 7-demicube is added with half
B7_polytope
Japanese production continuous improvement process
and then asks the owner of the shop to perform a quick kaizen (5S) to rectify those issues, or a line worker who notices a potential improvement in efficiency
Kaizen
constructed as an alternation of the regular 6-cube honeycomb. It is composed of two different types of facets. The 6-cubes become alternated into 6-demicubes h{4
6-demicubic_honeycomb
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