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regular 24-cell. There are two degrees of truncations, including a bitruncation. The truncated 24-cell or truncated icositetrachoron is a uniform 4-dimensional
Truncated_24-cells
octahedral cells correspond with the cells of a 24-cell and its dual. E. L. Elte identified it in 1912 as a semiregular polytope. Runcinated 24-cell (Norman
Runcinated_24-cells
represented by different arrangements of colored truncated 24-cell facets. In all cases, four truncated 24-cells, and one tesseract meet at each vertex, but
Truncated_24-cell_honeycomb
Type of tesseract
which creates the truncated 16-cell. The truncated tesseract is bounded by 24 cells: 8 truncated cubes, and 16 tetrahedra. Truncated tesseract (Norman
Truncated_tesseract
Geometric figure
5-cell honeycomb or pentachoric-dispentachoric honeycomb is a space-filling tessellation honeycomb. It is composed of 5-cells and rectified 5-cells facets
5-cell_honeycomb
vertices are deleted, the 24 truncated octahedron cells become 24 icosahedron cells, the 24 cubes become 24 tetrahedron cells, and the 96 deleted vertex
Snub_24-cell
Uniform 4-polytope
bitruncated 120-cell or hexacosihecatonicosachoron is a uniform 4-polytope. It has 720 cells: 120 truncated icosahedra, and 600 truncated tetrahedra. Its
Truncated_120-cells
Removal of alternate vertices
4-polytope An alternated truncated 24-cell is the snub 24-cell. 4-honeycombs: An alternated truncated 24-cell honeycomb is the snub 24-cell honeycomb. A hypercube
Alternation_(geometry)
colors of cells, 8 for each. The rectified 24-cell can be derived from the 24-cell by the process of rectification: the 24-cell is truncated at the midpoints
Rectified_24-cell
degrees of truncations, including a bitruncation. The truncated 5-cell, truncated pentachoron or truncated 4-simplex is bounded by 10 cells: 5 tetrahedra
Truncated_5-cell
Class of 4-dimensional polytopes
of the cantitruncated 16-cell or truncated 24-cell, with the half symmetry group [(3,3)+,4]. The truncated octahedral cells become icosahedra. The cubes
Uniform_4-polytope
16-cell prism, Truncated 16-cell prism, Runcitruncated 16-cell prism 24-cell prism, rectified 24-cell prism, truncated 24-cell prism, cantellated 24-cell
List of polygons, polyhedra and polytopes
List_of_polygons,_polyhedra_and_polytopes
is a convex uniform 4-polytope, composed of 2640 cells: 120 truncated icosidodecahedra, 600 truncated octahedra, 720 decagonal prisms, and 1200 hexagonal
Runcinated_120-cells
Regular tessellation in 4D Euclidean space
in 4-space: Truncated 5-cell honeycomb Omnitruncated 5-cell honeycomb Truncated 24-cell honeycomb Rectified 24-cell honeycomb Snub 24-cell honeycomb The
24-cell_honeycomb
Rectified 600-cell, Truncated 600-cell, Cantellated 600-cell Prismatic uniform polychoron Grand antiprism Duoprism Tetrahedral prism, Truncated tetrahedral prism
List_of_mathematical_shapes
cuboctahedra corresponding with the cells of a 24-cell, 24 truncated cubes corresponding with the cells of the dual 24-cell, and 96 triangular prisms corresponding
Cantellated_24-cells
omnitruncated 16-cell, or great disprismatotesseractihexadecachoron is bounded by 80 cells: 8 truncated cuboctahedra, 16 truncated octahedra, 24 octagonal prisms
Runcinated_tesseracts
N-dimensional polytope with vertices adjacent to N facets
the truncated tetrahedron, truncated cube, truncated octahedron, truncated cuboctahedron, truncated dodecahedron, truncated icosahedron, and truncated icosidodecahedron
Simple_polytope
24-cell honeycomb, or snub icositetrachoric honeycomb is a uniform space-filling tessellation (or honeycomb) by snub 24-cells, 16-cells, and 5-cells.
Snub_24-cell_honeycomb
Minkowsi sum of line segments
perpendicular equal length line segments), the omnitruncated 5-cell, and the truncated 24-cell. Every permutohedron is a zonotope. Fix a zonotope Z {\displaystyle
Zonotope
Regular object in four dimensional geometry
tetrahedral cells of the 16-cell which become 16 octahedra, giving the 24-cell 24 octahedral cells. The 12 axes and 16 hexagons of the 24-cell constitute
24-cell
Four-dimensional geometrical object
bitruncated 5-cell. The runcitruncated 5-cell or prismatorhombated pentachoron is composed of 60 vertices, 150 edges, 120 faces, and 30 cells. The cells are: 5
Runcinated_5-cell
Isogonal polytope with uniform facets
Faces are truncated, doubling their edges. (The term, coined by Kepler, comes from Latin truncare 'to cut off'.) There are higher truncations also: bitruncation
Uniform_polytope
4D geometry item
cantitruncated 600-cell is a uniform 4-polytope. It is composed of 1440 cells: 120 truncated icosahedra, 720 pentagonal prisms and 600 truncated octahedra. It
Cantellated_120-cell
4-faces (6 5-cell and 6 truncated 5-cells). Truncated hexateron (Acronym: tix) (Jonathan Bowers) The vertices of the truncated 5-simplex can be most simply
Truncated_5-simplexes
Primitive cell of crystal lattices with Voronoi decomposition applied
points. As in the case of all primitive cells, all area or space within the lattice can be filled by Wigner–Seitz cells and there will be no gaps. Nearby lattice
Wigner–Seitz_cell
Five-dimensional geometric shape
24-cell honeycomb, with symbols {3,4,3,3}, . There are 31 reflective uniform honeycombs in this family, and one alternated form. Truncated 24-cell honeycomb
Uniform_5-polytope
24-cell honeycomb is a uniform space-filling honeycomb. It can be seen as a bitruncation of the regular 24-cell honeycomb, constructed by truncated tesseract
Bitruncated_24-cell_honeycomb
Archimedean solid with 14 faces
the truncated cube, or truncated hexahedron, is an Archimedean solid. It has 14 regular faces (6 octagonal and 8 triangular), 36 edges, and 24 vertices
Truncated_cube
Regular paracompact honeycomb
triangular prism cells, with a wedge vertex figure. The cantitruncated hexagonal tiling honeycomb, t0,1,2{6,3,3}, has truncated tetrahedron, truncated trihexagonal
Hexagonal_tiling_honeycomb
Euclidean 4-space. It is constructed by 24-cell and truncated 16-cell facets. Truncated hexadecachoric tetracomb / Truncated hexadecachoric honeycomb The [3,4
Truncated_16-cell_honeycomb
Archimedean solid with 14 faces
field of graph theory, a truncated octahedral graph is the graph of vertices and edges of the truncated octahedron. It has 24 vertices and 36 edges, and
Truncated_octahedron
Regular tiling of hyperbolic 3-space
regular honeycombs: The truncated icosahedral honeycomb, t0,1{3,5,3}, , has alternating dodecahedron and truncated icosahedron cells, with a triangular pyramid
Icosahedral_honeycomb
Geometric operation applied to a polyhedron
24-cell. It is instead actually an alternated truncated 24-cell. Coxeter's snub terminology is slightly different, meaning an alternated truncation,
Snub_(geometry)
cantitruncated 24-cell honeycomb is a uniform space-filling honeycomb. It can be seen as a cantitruncation of the regular 24-cell honeycomb, containing truncated tesseract
Cantitruncated 24-cell honeycomb
Cantitruncated_24-cell_honeycomb
Only regular space-filling tessellation of the cube
cuboctahedrille, and its dual an oblate octahedrille. The truncated cubic honeycomb or truncated cubic cellulation is a uniform space-filling tessellation
Cubic_honeycomb
(and D4 lattice) is 24 and its Voronoi tessellation is a 24-cell honeycomb, , containing all rectified 16-cells (24-cell) Voronoi cells, or . There are three
16-cell_honeycomb
Convex uniform 4-polytope
uniform 4-dimensional polytope) that is bounded by 56 cells: 8 truncated cuboctahedra, 16 truncated tetrahedra, and 32 triangular prisms. The cantitruncated
Cantellated_tesseract
Operation in Euclidean geometry
r} will have its {p, q} cells bitruncated into truncated {q, p} cells, and the vertices are replaced by truncated {q, r} cells. An interesting result of
Bitruncation
honeycomb 24-cell honeycomb Truncated 24-cell honeycomb Snub 24-cell honeycomb 5-cell honeycomb Truncated 5-cell honeycomb Omnitruncated 5-cell honeycomb
Truncated tesseractic honeycomb
Truncated_tesseractic_honeycomb
geometry, a truncated 6-cube (or truncated hexeract) is a convex uniform 6-polytope, being a truncation of the regular 6-cube. There are 5 truncations for the
Truncated_6-cubes
The cells are: 5 truncated octahedra, 10 triangular prisms, and 5 truncated tetrahedra. Each vertex is surrounded by 2 truncated octahedra, one triangular
Cantellated_5-cell
Mathematical foam of equal-volume bubbles
cells of minimum surface area than the previous best-known solution, the Kelvin structure. In two dimensions, the subdivision of the plane into cells
Weaire–Phelan_structure
16-cell honeycomb 24-cell honeycomb Rectified 24-cell honeycomb Truncated 24-cell honeycomb Snub 24-cell honeycomb 5-cell honeycomb Truncated 5-cell honeycomb
Bitruncated_16-cell_honeycomb
triangles removed as holes. It is dual to the truncated cubic honeycomb with octahedral and truncated cubic cells: If the square pyramids of the pyramidille
Tetragonal disphenoid honeycomb
Tetragonal_disphenoid_honeycomb
tetrahedral cells of the 8-simplex. Truncated enneazetton (Acronym: tene) (Jonathan Bowers) The Cartesian coordinates of the vertices of the truncated 8-simplex
Truncated_8-simplexes
Genetically engineered T cell
Chimeric antigen receptor T cells (CAR T cells)—also known as chimeric immunoreceptors, chimeric T cell receptors or artificial T cell receptors—are receptor
CAR_T_cell
6-orthoplex are located inside the tetrahedral cells of the 6-orthoplex. Truncated hexacross Truncated hexacontatetrapeton (Acronym: tag) (Jonathan Bowers)
Truncated_6-orthoplexes
Shape with six sides
the truncated tetrahedron, truncated octahedron, truncated icosahedron (of soccer ball and fullerene fame), truncated cuboctahedron and the truncated icosidodecahedron
Hexagon
16-cell honeycomb 24-cell honeycomb Rectified 24-cell honeycomb Truncated 24-cell honeycomb Snub 24-cell honeycomb 5-cell honeycomb Truncated 5-cell honeycomb
Birectified_16-cell_honeycomb
16-cell honeycomb 24-cell honeycomb Truncated 24-cell honeycomb Snub 24-cell honeycomb 5-cell honeycomb Truncated 5-cell honeycomb Omnitruncated 5-cell honeycomb
Rectified_24-cell_honeycomb
Quasiregular space-filling tesselation
honeycomb is the dual of the triakis truncated tetrahedral honeycomb, with triakis truncated tetrahedral cells. For an alternated cubic honeycomb, with
Tetrahedral-octahedral honeycomb
Tetrahedral-octahedral_honeycomb
forms are given below, including dual configurations from the two regular 24-cells. (The dual configurations are named in bold.) Active rings in the first
List_of_F4_polytopes
Tiling of euclidean or hyperbolic space of three or more dimensions
gyrated triangular prismatic honeycomb The triakis truncated tetrahedral honeycomb. The Voronoi cells of the carbon atoms in diamond are this shape. The
Honeycomb_(geometry)
Uniform polychoron
four-dimensional geometry, the rectified 5-cell is a uniform 4-polytope composed of 5 regular tetrahedral and 5 regular octahedral cells. Each edge has one tetrahedron
Rectified_5-cell
rectified tesseract, truncated tetrahedral alterprism, or truncated tetrahedral cupoliprism, s3{2,4,3}, . It is made from 2 truncated tetrahedra, 6 tetrahedra
Rhombicuboctahedral_prism
Isogonal polyhedron with regular faces
the five truncations of the Platonic solids—truncated tetrahedron, truncated octahedron, truncated cube, truncated dodecahedron, and truncated icosahedron—and
Uniform_polyhedron
Polygon shape with eight sides
also be constructed as a quasiregular truncated square, t{4}, which alternates two types of edges. A truncated octagon, t{8} is a hexadecagon, {16}. A
Octagon
Four-dimensional analog of the icosahedron
Five 24-cells meet at each 600-cell vertex, so all 25 24-cells are linked by each great pentagon. The 600-cell can be partitioned into five disjoint 24-cells
600-cell
Operation in Euclidean geometry
cells {p,q}. Its rectification will have two cell types, a rectified {p,q} polyhedron left from the original cells and {q,r} polyhedron as new cells formed
Rectification_(geometry)
uniform honeycomb in hyperbolic 3-space. It has truncated square tiling, truncated cuboctahedron, and truncated octahedron facets in a mirrored sphenoid vertex
Square_tiling_honeycomb
diagram perspective projections, centered on the cell at pos. 3, with a consistent orientation, and the 16 cells at position 0 are shown solid, alternately
B4_polytope
Geometric figure
24-cell honeycomb Truncated 24-cell honeycomb Snub 24-cell honeycomb 5-cell honeycomb Truncated 5-cell honeycomb Omnitruncated 5-cell honeycomb Coxeter
Omnitruncated tesseractic honeycomb
Omnitruncated_tesseractic_honeycomb
honeycomb 24-cell honeycomb Truncated 24-cell honeycomb Snub 24-cell honeycomb 5-cell honeycomb Truncated 5-cell honeycomb Omnitruncated 5-cell honeycomb
Bitruncated tesseractic honeycomb
Bitruncated_tesseractic_honeycomb
Tiling of hyperbolic 3-space by uniform polyhedra
vertex figure, it can furthermore be truncated, producing a uniform honeycomb with truncated dodecahedra, truncated great dodecahedra, and small ditrigonal
Uniform honeycombs in hyperbolic space
Uniform_honeycombs_in_hyperbolic_space
Notation for polytopes and tessellations
4-polytopes. For example, the 120-cell is represented by {5,3,3}. It is made of dodecahedral cells {5,3}, and has 3 cells around each edge. There is one
Schläfli_symbol
Prism with a 6-sided base
hexagonal prism also exists as cells of four prismatic uniform convex honeycombs in 3 dimensions: It also exists as cells of a number of four-dimensional
Hexagonal_prism
edge length. A regular 5-cell is formed at each truncated vertex. The Cartesian coordinates of the vertices of a truncated 5-cube having edge length 2
Truncated_5-cubes
Convex uniform 8-polytope in 8-dimensional geometry
located inside the cubic cells of the 8-cube. The final truncations are best expressed relative to the 8-orthoplex. Truncated octeract (acronym: tocto)
Truncated_8-cubes
7-polytope
tetrahedral cells of the 7-orthoplex. The final three truncations are best expressed relative to the 7-cube. Truncated heptacross Truncated hecatonicosaoctaexon
Truncated_7-orthoplexes
third and fourth truncations are more easily constructed as second and first truncations of the 5-cube. Truncated pentacross Truncated triacontaditeron
Truncated_5-orthoplexes
Uniform 7- polytope
located inside the cubic cells of the 7-cube. The final three truncations are best expressed relative to the 7-orthoplex. Truncated hepteract (Jonathan Bowers)
Truncated_7-cubes
symmetry families. there is also one half symmetry alternation, the snub 24-cell. Each can be visualized as symmetric orthographic projections in Coxeter
D4_polytope
Four-dimensional analog of the dodecahedron
so the 120-cell is the convex hull of 25 disjoint 24-cells. Each 24-cell is the convex hull of 3 disjoint (8-point) 16-cells, so the 120-cell is the convex
120-cell
with 6 truncated tetrahedra and 2 tetrahedra around each vertex. It is one of the 28 convex uniform honeycombs. The faces of this honeycomb's cells form
Quarter_cubic_honeycomb
16-cell honeycomb 24-cell honeycomb Rectified 24-cell honeycomb Truncated 24-cell honeycomb Snub 24-cell honeycomb 5-cell honeycomb Truncated 5-cell honeycomb
Steric_tesseractic_honeycomb
16-cell honeycomb 24-cell honeycomb Rectified 24-cell honeycomb Truncated 24-cell honeycomb Snub 24-cell honeycomb 5-cell honeycomb Truncated 5-cell honeycomb
Stericantic tesseractic honeycomb
Stericantic_tesseractic_honeycomb
Uniform 7-polytope
tetrahedral cells of the 7-simplex. In seven-dimensional geometry, a truncated 7-simplex is a convex uniform 7-polytope, being a truncation of the regular
Truncated_7-simplexes
Lossy color image compression algorithm
tables should be used. A histogram of all the 24-bit colors in the original 24-bit color image, or the truncated 15-bit color vectors, is created. In a naïve
Color_Cell_Compression
Regular 5-polytope
the pyramid are made of 5-cell cells. These are seen as vertex figures of truncated regular 6-polytopes, like a truncated 6-cube. Another form is {3
5-simplex
Tessalating shape in four dimensional space
honeycomb 24-cell honeycomb Truncated 24-cell honeycomb Snub 24-cell honeycomb 5-cell honeycomb Truncated 5-cell honeycomb Omnitruncated 5-cell honeycomb
Rectified tesseractic honeycomb
Rectified_tesseractic_honeycomb
Polygon with 12 edges
the Schläfli symbol {12} and can be constructed as a truncated hexagon, t{6}, or a twice-truncated triangle, tt{3}. The internal angle at each vertex of
Dodecagon
Uniform space-filling tessellation in Euclidean 4-space
honeycomb 24-cell honeycomb Truncated 24-cell honeycomb Snub 24-cell honeycomb 5-cell honeycomb Truncated 5-cell honeycomb Omnitruncated 5-cell honeycomb
Cantitruncated tesseractic honeycomb
Cantitruncated_tesseractic_honeycomb
Polygon with 24 edges
Schläfli symbol {24} and can also be constructed as a truncated dodecagon, t{12}, or a twice-truncated hexagon, tt{6}, or thrice-truncated triangle, ttt{3}
Icositetragon
Gastrointestinal peptide hormone involved in glucose homeostasis
several organs, including the pancreas (α-cells of the islets of Langerhans), gut (intestinal enteroendocrine L-cells) and brain (caudal brainstem and hypothalamus)
Glucagon-like_peptide-1
located inside the tetrahedral cells of the 8-orthoplex. The final truncations are best expressed relative to the 8-cube. Truncated octacross (acronym: tek)
Truncated_8-orthoplexes
and truncated tetrahedral cells. In 4-dimensions it is called a cyclotruncated 5-cell honeycomb, with Coxeter graph , with 5-cell, truncated 5-cell, and
Cyclotruncated simplicial honeycomb
Cyclotruncated_simplicial_honeycomb
Catalan solid with 12 faces
center; these form the images of six pairs of the 24-cell's octahedral cells. The remaining 12 octahedral cells project onto the faces of the rhombic dodecahedron
Rhombic_dodecahedron
Uniform 6-polytope
can be derived by mirror removal and ratios of Coxeter group orders. Truncated 122 polytope (Acronym: tim) Its construction is based on the E6 group
1_22_polytope
Uniform 6-polytope
The truncated 221 has 432 vertices, 2376 edges, 5040 faces, 4320 cells, 1350 4-faces, and 126 5-faces. Its vertex figure is a rectified 5-cell pyramid
2_21_polytope
16-cell honeycomb 24-cell honeycomb Rectified 24-cell honeycomb Truncated 24-cell honeycomb Snub 24-cell honeycomb 5-cell honeycomb Truncated 5-cell honeycomb
Steriruncic tesseractic honeycomb
Steriruncic_tesseractic_honeycomb
16-cell honeycomb 24-cell honeycomb Rectified 24-cell honeycomb Snub 24-cell honeycomb 5-cell honeycomb Truncated 5-cell honeycomb Omnitruncated 5-cell honeycomb
Stericated_24-cell_honeycomb
16-cell honeycomb 24-cell honeycomb Rectified 24-cell honeycomb Snub 24-cell honeycomb 5-cell honeycomb Truncated 5-cell honeycomb Omnitruncated 5-cell honeycomb
Cantellated_24-cell_honeycomb
Solid with 2 parallel n-gonal bases connected by n parallelograms
the geometrical truncation of an n-gonal hosohedron, as well as through the cantellation or expansion of an n-gonal dihedron. A truncated prism is formed
Prism_(geometry)
honeycomb 24-cell honeycomb Truncated 24-cell honeycomb Snub 24-cell honeycomb 5-cell honeycomb Truncated 5-cell honeycomb Omnitruncated 5-cell honeycomb
Cantellated tesseractic honeycomb
Cantellated_tesseractic_honeycomb
16-cell honeycomb 24-cell honeycomb Rectified 24-cell honeycomb Snub 24-cell honeycomb 5-cell honeycomb Truncated 5-cell honeycomb Omnitruncated 5-cell honeycomb
Runcinated_24-cell_honeycomb
honeycomb 24-cell honeycomb Truncated 24-cell honeycomb Snub 24-cell honeycomb 5-cell honeycomb Truncated 5-cell honeycomb Omnitruncated 5-cell honeycomb
Runcinated tesseractic honeycomb
Runcinated_tesseractic_honeycomb
3rd order truncations (runcination) of the regular 6-cube. There are 12 unique runcinations of the 6-cube with permutations of truncations, and cantellations
Runcinated_6-cubes
honeycomb 24-cell honeycomb Truncated 24-cell honeycomb Snub 24-cell honeycomb 5-cell honeycomb Truncated 5-cell honeycomb Omnitruncated 5-cell honeycomb
Runcitruncated tesseractic honeycomb
Runcitruncated_tesseractic_honeycomb
Compound polyhedron
disjoint 600-cells, and each of its dodecahedral cells is a compound of 5 tetrahedral cells, one cell from each of the 5 disjoint 600-cells. Compound of
Compound_of_five_tetrahedra
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TRUNCATED 24-CELLS
TRUNCATED 24-CELLS
TRUNCATED 24-CELLS
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