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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
Type of tesseract
In geometry, a truncated tesseract is a uniform 4-polytope formed as the truncation of the regular tesseract. There are three truncations, including a
Truncated_tesseract
In geometry, the rectified 24-cell or rectified icositetrachoron is a uniform 4-dimensional polytope (or uniform 4-polytope), which is bounded by 48 cells:
Rectified_24-cell
runcinated tesseract (or runcinated 16-cell) is a convex uniform 4-polytope, being a runcination (a 3rd order truncation) of the regular tesseract. There
Runcinated_tesseracts
4-polytope Rectified 5-cell, Truncated 5-cell, Cantellated 5-cell, Runcinated 5-cell Rectified tesseract, Truncated tesseract, Cantellated tesseract, Runcinated
List_of_mathematical_shapes
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
located in the tesseract centers of the 9-cube. These polytopes are part of a family of 511 uniform 9-polytopes with BC9 symmetry. Rectified enneract (Acronym:
Rectified_9-cubes
Regular object in four dimensional geometry
regular polytope, 5-cell, the 24-cell is self-dual. The 24-cell and the tesseract are the only convex regular 4-polytopes in which the edge length equals
24-cell
runcination of a tesseractic honeycomb creating runcinated tesseracts, and new tesseract, rectified tesseract and cuboctahedral prism facets. The [4,3,3,4], , Coxeter
Runcinated tesseractic honeycomb
Runcinated_tesseractic_honeycomb
regular 24-cell honeycomb, containing tesseract and rectified 24-cell cells. Rectified icositetrachoric tetracomb Rectified icositetrachoric honeycomb Cantellated
Rectified_24-cell_honeycomb
4-polytope Rectified 5-cell, Truncated 5-cell, Cantellated 5-cell, Runcinated 5-cell Rectified tesseract, Truncated tesseract, Cantellated tesseract, Runcinated
List of polygons, polyhedra and polytopes
List_of_polygons,_polyhedra_and_polytopes
Convex uniform 4-polytope
geometry, a cantellated tesseract is a convex uniform 4-polytope, being a cantellation (a 2nd order truncation) of the regular tesseract. There are four degrees
Cantellated_tesseract
Operation in Euclidean geometry
the rectified cube, also called a cuboctahedron, and also represented as { 4 3 } {\displaystyle {\begin{Bmatrix}4\\3\end{Bmatrix}}} . And a rectified cuboctahedron
Rectification_(geometry)
Tessalating shape in four dimensional space
new vertices on the middle of all the original edges, rectifying the cells into rectified tesseracts, and adding new 16-cell facets at the original vertices
Rectified tesseractic honeycomb
Rectified_tesseractic_honeycomb
Four Dimensions, George Olshevsky. Convex uniform polychora based on the tesseract/16-cell, George Olshevsky. Convex uniform polychora based on the 24-cell
D4_polytope
Notation for polytopes and tessellations
polyhedral cells around each edge is represented by {p,q,r}. For example, a tesseract, {4,3,3}, has 3 cubes, {4,3}, around an edge. In general, a regular polytope
Schläfli_symbol
Name tesseract rectified tesseract truncated tesseract cantellated tesseract runcinated tesseract bitruncated tesseract cantitruncated tesseract runcitruncated
Truncated_24-cells
Isogonal polytope with uniform facets
solids (excluding the cube-prism, which has already been counted as the tesseract), and two infinite sets: the prisms on the convex antiprisms, and the
Uniform_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
uniform 4-polytopes with B4 symmetry. There are two regular forms, the tesseract and 16-cell, with 16 and 8 vertices respectively. They can be visualized
B4_polytope
Geometric space with five dimensions
faces (each a square), 40 cells (each a cube), and 10 hypercells (each a tesseract). The 5-orthoplex of the cross polytope family, {3,3,3,4}, with 10 vertices
Five-dimensional_space
the runcic snub cubic hosochoron, also known as a parabidiminished rectified tesseract, truncated tetrahedral alterprism, or truncated tetrahedral cupoliprism
Rhombicuboctahedral_prism
seen as a cantellation of the regular 24-cell honeycomb, containing rectified tesseract, cantellated 24-cell, and tetrahedral prism cells. Cantellated icositetrachoric
Cantellated_24-cell_honeycomb
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
cantitruncation of the regular 24-cell honeycomb, containing truncated tesseract, cantitruncated 24-cell, and tetrahedral prism cells. Cantellated icositetrachoric
Cantitruncated 24-cell honeycomb
Cantitruncated_24-cell_honeycomb
be seen as a truncation of the regular 24-cell honeycomb, containing tesseract and truncated 24-cell cells. It has a uniform alternation, called the
Truncated_24-cell_honeycomb
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
edge or only a face. The vertex figure of the 24-cell honeycomb is a tesseract (4-dimensional cube). So there are 16 edges, 32 triangles, 24 octahedra
24-cell_honeycomb
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
runcination of the regular 16-cell honeycomb, containing Rectified 24-cell, runcinated tesseract, cuboctahedral prism, and 3-3 duoprism cells. Runcinated
Runcinated_16-cell_honeycomb
10-polytopes with BC10 symmetry. Rectified dekeract (Acronym: rade) (Jonathan Bowers) Cartesian coordinates for the vertices of a rectified 10-cube, centered at the
Rectified_10-cubes
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
constructed from this honeycomb. or rectified heptacross rectified hecatonicosaoctaexon (Acronym: rez) (Jonathan Bowers) - rectified 128-faceted polyexon There
Rectified_7-orthoplexes
Uniform 6-polytope
(dual of E6 lattice). Birectified 221 polytope Rectified pentacontatetrapeton (Acronym: ram) - rectified 54-facetted polypeton (Jonathan Bowers) Vertices
1_22_polytope
in 4-space: Tesseractic honeycomb 16-cell honeycomb 24-cell honeycomb Rectified 24-cell honeycomb Truncated 24-cell honeycomb Snub 24-cell honeycomb 5-cell
Birectified_16-cell_honeycomb
centers of the 7-cube. rectified hepteract (acronym: rasa) (Jonathan Bowers) Cartesian coordinates for the vertices of a rectified 7-cube, centered at the
Rectified_7-cubes
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
Regular paracompact honeycomb
of a sequence of regular polychora, which include the 5-cell {3,3,3}, tesseract {4,3,3}, and 120-cell {5,3,3} of Euclidean 4-space, along with other hyperbolic
Hexagonal_tiling_honeycomb
Regular tiling of hyperbolic 3-space
first polytope in the sequence is the tesseract, and the second is the Euclidean cubic honeycomb. The rectified order-5 cubic honeycomb, , has alternating
Order-5_cubic_honeycomb
in the square face centers of the 5-cube. Rectified penteract (acronym: rin) (Jonathan Bowers) The rectified 5-cube may be constructed from the 5-cube
Rectified_5-cubes
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
as a first rectification of a 5-dimensional cross polytope. Rectified pentacross Rectified triacontaditeron (32-faceted 5-polytope) Acronym: rat (Jonathan
Rectified_5-orthoplexes
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
bitruncation of the regular 24-cell honeycomb, constructed by truncated tesseract and bitruncated 24-cell cells. Bitruncated icositetrachoric tetracomb/honeycomb
Bitruncated_24-cell_honeycomb
A5 [6] D3 / A3 [4] 1 221 Icosihepta-heptacontadipeton (jak) 2 Rectified 221 Rectified icosihepta-heptacontadipeton (rojak) 3 Trirectified 221 Trirectified
E6_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
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
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
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
the 6-orthoplex. The rectified 6-orthoplex is the vertex figure for the demihexeractic honeycomb. or Rectified hexacross Rectified hexacontatetrapeton
Rectified_6-orthoplexes
Geometrical Shape
in the square face centers of the 6-cube. Rectified hexeract (acronym: rax) (Jonathan Bowers) The rectified 6-cube may be constructed from the 6-cube
Rectified_6-cubes
Concept in euclidean geometry
3,4}, and consisting of a packing of tesseracts (4-hypercubes). Its vertex figure is a 16-cell. Two tesseracts meet at each cubic cell, four meet at
Tesseractic_honeycomb
vertex. Alternative names: Rectified 120-cell (Norman Johnson) Rectified hecatonicosichoron / rectified dodecacontachoron / rectified polydodecahedron Icosidodecahedral
Rectified_120-cell
9-polytopes with BC9 symmetry. The rectified 9-orthoplex is the vertex figure for the demienneractic honeycomb. or Rectified enneacross (Acronym: riv) (Jonathan
Rectified_9-orthoplexes
Octahedron centered Dual octahedron centered 1 24-cell (rectified 16-cell) = {3,4,3} = r{3,3,4} 2 rectified 24-cell (cantellated 16-cell) = r{3,4,3} = rr{3,3
List_of_F4_polytopes
Tetrahedron centered Dual tetrahedron centered 1 5-cell pentachoron {3,3,3} 2 rectified 5-cell r{3,3,3} 3 truncated 5-cell t{3,3,3} 4 cantellated 5-cell rr{3
A4_polytope
Solid with 2 parallel n-gonal bases connected by n parallelograms
product {p,q}×{ }. If the polyhedron and the sides are cubes, it becomes a tesseract: {4,3}×{ } = {4,3,3}. Example: , Dodecahedral prism, {5,3}×{ }, two parallel
Prism_(geometry)
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
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
Type of geometric object
the 5-cell centers of the 9-simplex. The rectified 9-simplex is the vertex figure of the 10-demicube. Rectified decayotton (reday) (Jonathan Bowers) The
Rectified_9-simplexes
ten-dimensional geometry, a rectified 10-orthoplex is a 10-polytope, being a rectification of the regular 10-orthoplex. The rectified 10-orthoplex is the vertex
Rectified_10-orthoplexes
Removal of alternate vertices
alternated into a uniform demihypercube. Cube → Tetrahedron (regular) → Tesseract (8-cell) → 16-cell (regular) → Penteract → demipenteract (semiregular)
Alternation_(geometry)
simple Lie groups. The rectified 8-orthoplex is the vertex figure for the demiocteractic honeycomb. or Rectified octacross Rectified diacosipentacontahexazetton
Rectified_8-orthoplexes
Uniform 8-polytope
truncated 7-simplexes 128 rectified 7-simplexes 6-faces 112 truncated 6-demicubes 1024 truncated 6-simplexes 1024 rectified 6-simplexes 1024 6-simplexes
Cantic_8-cube
Type of uniform 4-polytope in four-dimensional geography
which 18 are convex; one of these, the cube-prism, is listed above as the tesseract).[citation needed] There are 18 convex polyhedral prisms created from
Prismatic_uniform_4-polytope
64 truncated 6-simplexes 64 rectified 6-simplexes 5-faces 84 truncated 5-demicubes 448 truncated 5-simplexes 448 rectified 5-simplexes 448 5-simplexes
Cantic_7-cube
[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
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
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
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
Geometric prism
one of four four-dimensional Hanner polytopes; the other three are the tesseract, the 16-cell, and the dual of the octahedral prism (a cubical bipyramid)
Octahedral_prism
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
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
4D geometry item
Cantellated tetrahedron (Cuboctahedron) 1 1200 None (Degenerate triangular prism) 2 720 Pentagonal prism 3 120 Rectified dodecahedron (Icosidodecahedron)
Cantellated_120-cell
{4,3,3,3} 5-cube Penteract (pent) 3 t1{4,3,3,3} = r{4,3,3,3} Rectified 5-cube Rectified penteract (rin) 4 t2{4,3,3,3} = 2r{4,3,3,3} Birectified 5-cube
B5_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
Uniform 6-dimensional polytope
Rectified 6-simplex Cantellated 6-simplex Runcinated 6-simplex Stericated 6-simplex Pentellated 6-simplex 6-orthoplex Truncated 6-orthoplex Rectified
Uniform_6-polytope
Four-dimensional analogue of the tetrahedron
edges is the characteristic orthoscheme of the 4-cube (also called the tesseract or 8-cell), the 4-dimensional analogue of the 3-dimensional cube. If the
5-cell
A3 / D3 [4] 1 231 (laq) 2 Rectified 231 (rolaq) 3 Rectified 132 (rolin) 4 132 (lin) 5 Birectified 321 (branq) 6 Rectified 321 (ranq) 7 321 (naq) 8 Truncated
E7_polytope
Polyhedron with non-planar faces
produces a n-n duoprism, and specifically {4,4|4} fits inside of a {4}x{4} tesseract. A final set is based on Coxeter's further extended form {q1,m|q2,q3.
Regular_skew_polyhedron
Uniform 8 dimensional polytope
polytope Quadrirectified 421 polytope Rectified diacositetraconta-dischiliahectohexaconta-zetton as a rectified 240-2160 facetted polyzetton (acronym:
1_42_polytope
1 t0{3,3,3,3,3} 6-simplex Heptapeton (hop) 2 t1{3,3,3,3,3} Rectified 6-simplex Rectified heptapeton (ril) 3 t0,1{3,3,3,3,3} Truncated 6-simplex Truncated
A6_polytope
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
H4 family polytopes 120-cell rectified 120-cell truncated 120-cell cantellated 120-cell runcinated 120-cell cantitruncated 120-cell runcitruncated 120-cell
Runcinated_120-cells
Four-dimensional geometric object with flat sides
There are only 3 cases identified by Thorold Gosset in 1900: the rectified 5-cell, rectified 600-cell, and snub 24-cell. A 4-polytope is uniform if it has
4-polytope
Chatbot developed by Google
roots in Gemini's training corpus and algorithms, making it difficult to rectify. Jeremy Kahn of Fortune called for researchers focused on safety and responsibility
Google_Gemini
Polyhedron formed by joining mirroring pyramids base-to-base
polygon base is a rhombus. Given numerically due to more complex form. The rectified 16-cell is the regular 24-cell and vertices are all equivalent – octahedra
Bipyramid
8-simplex Truncated 8-simplex Rectified 8-simplex Quadritruncated 8-simplex Tritruncated 8-simplex Bitruncated 8-simplex Orthogonal projections in A8
Truncated_8-simplexes
Isogonal polyhedron with regular faces
regular polyhedron, and a triangular antiprism. The octahedron is also a rectified tetrahedron. Many polyhedra are repeated from different construction sources
Uniform_polyhedron
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
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
Solid with eight equal triangular faces
equilateral triangles. The regular octahedron can also be considered a rectified tetrahedron, sometimes called a tetratetrahedron (by analogy to the cuboctahedron
Regular_octahedron
Uniform 8 dimensional polytope
0,1} 8960 {3,3} Faces 7168 {3} Edges 1792 Vertices 128 Vertex figure Rectified 7-simplex Symmetry group D8, [35,1,1] = [1+,4,36] A18, [27]+ Dual ? Properties
8-demicube
Regular 5-polytope
40 {31,0,1} 80 {3,3} Faces 160 {3} Edges 80 Vertices 16 Vertex figure Rectified 5-cell Petrie polygon Octagon Symmetry D5, [32,1,1] = [1+,4,33] [24]+
5-demicube
Uniform 10-polytope
1} 107520 {3,3} Faces 61440 {3} Edges 11520 Vertices 512 Vertex figure Rectified 9-simplex Symmetry group D10, [37,1,1] = [1+,4,38] [29]+ Dual ? Properties
10-demicube
Uniform 9-polytope
1} 32256 {3,3} Faces 21504 {3} Edges 4608 Vertices 256 Vertex figure Rectified 8-simplex Symmetry group D9, [36,1,1] = [1+,4,37] [28]+ Dual ? Properties
9-demicube
3,4} 6-orthoplex Hexacontatetrapeton (gee) 2 t1{3,3,3,3,4} Rectified 6-orthoplex Rectified hexacontatetrapeton (rag) 3 t2{3,3,3,3,4} Birectified 6-orthoplex
B6_polytope
Four-dimensional analog of the icosahedron
deconstructed into three overlapping instances of its predecessor the tesseract (8-cell), and the 8-cell can be deconstructed into two instances of its
600-cell
coordinates coincide with the vertices of an inscribed runcitruncated tesseract. The dual configuration has all permutations and signs of: (0,2,2+√2,2+√2)
Cantellated_24-cells
2017 Android mobile operating system
2017. Retrieved September 14, 2017. "This New Android Oreo Feature Helps Rectify Bootloop Issues". NDTV Gadgets360. Archived from the original on September
Android_Oreo
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