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Regular object in four dimensional geometry
four-dimensional geometry, the 24-cell is a convex regular 4-polytope, a four-dimensional analogue of a Platonic solid. It is named for the 24 octahedra that form
24-cell
rectified 24-cell or rectified icositetrachoron is a uniform 4-dimensional polytope (or uniform 4-polytope), which is bounded by 48 cells: 24 cubes, and 24 cuboctahedra
Rectified_24-cell
the snub 24-cell or snub disicositetrachoron is a convex uniform 4-polytope composed of 120 regular tetrahedral and 24 icosahedral cells. Five tetrahedra
Snub_24-cell
Regular tessellation in 4D Euclidean space
In four-dimensional Euclidean geometry, the 24-cell honeycomb, or icositetrachoric honeycomb is a regular space-filling tessellation (or honeycomb) of
24-cell_honeycomb
Four-dimensional analog of the icosahedron
predecessor the 24-cell, as the 24-cell can be deconstructed into three overlapping instances of its predecessor the tesseract (8-cell), and the 8-cell can be
600-cell
geometry, a runcinated 24-cell is a convex uniform 4-polytope, being a runcination (a 3rd order truncation) of the regular 24-cell. There are 3 unique degrees
Runcinated_24-cells
geometry, a truncated 24-cell is a uniform 4-polytope (4-dimensional uniform polytope) formed as the truncation of the regular 24-cell. There are two degrees
Truncated_24-cells
Class of 4-dimensional polytopes
that all cells, faces, edges, and vertices are congruent: 6 regular convex 4-polytopes: 5-cell {3,3,3}, 8-cell {4,3,3}, 16-cell {3,3,4}, 24-cell {3,4,3}
Uniform_4-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
geometry, a cantellated 24-cell is a convex uniform 4-polytope, being a cantellation (a 2nd order truncation) of the regular 24-cell. There are 2 unique degrees
Cantellated_24-cells
4-dimensional packing of 16-cell facets, three around every (triangular) face. Its dual is the 24-cell honeycomb. Its vertex figure is a 24-cell. The vertex arrangement
16-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
Cantitruncated 24-cell honeycomb
Cantitruncated_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
Truncated_24-cell_honeycomb
Rectified 16-cell, Truncated 16-cell Rectified 24-cell, Truncated 24-cell, Cantellated 24-cell, Runcinated 24-cell, Snub 24-cell Rectified 120-cell, Truncated
List of polygons, polyhedra and polytopes
List_of_polygons,_polyhedra_and_polytopes
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
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
Bitruncated_24-cell_honeycomb
In the geometry of hyperbolic 5-space, the 24-cell honeycomb honeycomb is one of five paracompact regular space-filling tessellations (or honeycombs)
24-cell_honeycomb_honeycomb
Four-dimensional analog of the octahedron
multiple 16-cells: the 16-vertex tesseract as a compound of two 16-cells, the 24-vertex 24-cell as a compound of three 16-cells, the 120-vertex 600-cell as a
16-cell
Polygon with 12 edges
projections in Coxeter planes. Examples in 4 dimensions are the 24-cell, snub 24-cell, 6-6 duoprism, 6-6 duopyramid. In 6 dimensions 6-cube, 6-orthoplex
Dodecagon
Rectified 16-cell, Truncated 16-cell Rectified 24-cell, Truncated 24-cell, Cantellated 24-cell, Runcinated 24-cell, Snub 24-cell Rectified 120-cell, Truncated
List_of_mathematical_shapes
Five-dimensional geometric shape
Snub 24-cell honeycomb, with symbols s{3,4,3,3}, and constructed by four snub 24-cell, one 16-cell, and five 5-cells at each vertex. 16-cell honeycomb
Uniform_5-polytope
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
Four-dimensional analogue of the cube
eight cubical cells, meeting at right angles. The tesseract is one of the six convex regular 4-polytopes. The tesseract is also called an 8-cell, C8, (regular)
Tesseract
Natural number
the 24-dimensional Leech lattice. An icositetragon is a regular polygon with 24 sides. A tesseract has 24 two-dimensional square faces. The 24-cell, consisting
24_(number)
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
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
Sculpture in Pennsylvania State University's mathematics department
sculpture represents a mathematical object called the 24-cell or "octacube". Because a real 24-cell is four-dimensional, the artwork is actually a projection
Octacube_(sculpture)
Four-dimensional geometric object with flat sides
5-cell, rectified 600-cell, and snub 24-cell. A 4-polytope is uniform if it has a symmetry group under which all vertices are equivalent, and its cells
4-polytope
Basic unit of life forms
A biological cell basically consists of a semipermeable cell membrane enclosing cytoplasm that contains genetic material. Most cells are only visible
Cell_(biology)
Isogonal polytope with uniform facets
3,3]: the 5-cell {3,3,3}, which is self-dual; group [3,3,4]: 16-cell {3,3,4} and its dual tesseract {4,3,3}; group [3,4,3]: the 24-cell {3,4,3}, self-dual;
Uniform_polytope
In geometry, the dual snub 24-cell is a 144 vertex convex 4-polytope composed of 96 irregular cells. Each cell has faces of two kinds: three kites and
Dual_snub_24-cell
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
52-dimensional exceptional simple Lie group
of the 24-cell: it is a solvable group of order 1152. It has minimal faithful degree μ(G) = 24, which is realized by the action on the 24-cell. The group
F4_(mathematics)
In the geometry of hyperbolic 4-space, the order-4 24-cell honeycomb is one of two paracompact regular space-filling tessellations (or honeycombs). It
Order-4_24-cell_honeycomb
Geometric operation applied to a polyhedron
even-sided faces. In 4-dimensions, Conway suggests the snub 24-cell should be called a semi-snub 24-cell because, unlike 3-dimensional snub polyhedra are alternated
Snub_(geometry)
Removal of alternate vertices
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)
Type of tesseract
a tritruncation, which creates the truncated 16-cell. The truncated tesseract is bounded by 24 cells: 8 truncated cubes, and 16 tetrahedra. Truncated
Truncated_tesseract
Polygon with 24 edges
In geometry, an icositetragon (or icosikaitetragon) or 24-gon is a twenty-four-sided polygon. The sum of any icositetragon's interior angles is 3960 degrees
Icositetragon
Four-dimensional analogues of the regular polyhedra in three dimensions
regular star 4-polytopes: the grand 120-cell, great stellated 120-cell, grand 600-cell, and great grand stellated 120-cell. He skipped the remaining six because
Regular_4-polytope
In the geometry of hyperbolic 5-space, the order-4 24-cell honeycomb honeycomb is one of five paracompact regular space-filling tessellations (or honeycombs)
Order-4 24-cell honeycomb honeycomb
Order-4_24-cell_honeycomb_honeycomb
projective 4-polytopes. The 3 special cases are hemi-24-cell, hemi-600-cell, and hemi-120-cell. Only 2 of 3 regular spherical polytopes are centrally
List_of_regular_polytopes
Polytope with highest degree of symmetry
{3,3,...,3}. The regular 24-cell - {3,4,3} - in 4 dimensions. The great 120-cell - {5,5/2,5} - and grand stellated 120-cell - {5/2,5,5/2} - in 4 dimensions
Regular_polytope
symmetry, and one chiral half symmetry, the snub 24-cell. There is one self-dual regular form, the 24-cell with 24 vertices. Each can be visualized as symmetric
List_of_F4_polytopes
Four-dimensional analogue of the tetrahedron
the 5-cell is the convex 4-polytope with Schläfli symbol {3,3,3}. It is a 5-vertex four-dimensional object bounded by five tetrahedral cells. It is also
5-cell
Polyhedron with 8 triangles and 6 squares
24-cell honeycomb and the tesseractic honeycomb, respectively. Each tessellation has a dual tessellation; the cell centers in a tessellation are cell
Cuboctahedron
24-cell with construction = . Hexacosichoric group – H4, [5,3,3], (), order 14400, (Du Val #50 (I/I;I/I)*, Conway ±[I×I].2), named for the 600-cell (hexacosichoron)
Point groups in four dimensions
Point_groups_in_four_dimensions
Medical condition
Sickle cell disease (SCD), also simply called sickle cell, is a group of inherited hemoglobin-related blood disorders. Sickle cell disease is caused by
Sickle_cell_disease
Geometric figure
in 4-space: Tesseractic honeycomb 16-cell honeycomb 24-cell honeycomb Truncated 24-cell honeycomb Snub 24-cell honeycomb Olshevsky (2006), Model 134
5-cell_honeycomb
Device that converts the chemical energy from a fuel into electricity
A fuel cell is an electrochemical cell that converts the chemical energy of a fuel (often hydrogen) and an oxidizing agent (often oxygen) into electricity
Fuel_cell
Notation for polytopes and tessellations
{4,3}. A regular 4-dimensional polytope, with r {p,q} regular polyhedral cells around each edge is represented by {p,q,r}. For example, a tesseract, {4
Schläfli_symbol
4-D convex polytope
construction of the 24-cell. Thus, the 24-cell is constructed from exactly 16 cubic pyramids. The 24-cell tessellates 4-dimensional space as the 24-cell honeycomb
Cubic_pyramid
Uniform 6-polytope
related to the 24-cell by a geometric folding E6 → F4 of Coxeter-Dynkin diagrams, E6 corresponding to 122 in 6 dimensions, F4 to the 24-cell in 4 dimensions
1_22_polytope
Convex uniform 4-polytope
truncations. Two are also derived from the 24-cell family. The cantellated tesseract, bicantellated 16-cell, or small rhombated tesseract is a convex uniform
Cantellated_tesseract
rectified 600-cell or rectified hexacosichoron is a convex uniform 4-polytope composed of 600 regular octahedra and 120 icosahedra cells. Each edge has
Rectified_600-cell
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
Truncated_16-cell_honeycomb
4-D polyhedral pyramid
unit-edge-length 24-cell is 2, so the content of the regular octahedral pyramid is 1/12. The 24-cell tessellates 4-dimensional space as the 24-cell honeycomb.
Octahedral_pyramid
Concept in euclidean geometry
honeycombs in 4-space: 16-cell honeycomb 24-cell honeycomb 5-cell honeycomb Truncated 5-cell honeycomb Omnitruncated 5-cell honeycomb Baake, M.; Joseph
Tesseractic_honeycomb
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 as symmetric
B4_polytope
Uniform 4-polytope
In geometry, a truncated 120-cell is a uniform 4-polytope formed as the truncation of the regular 120-cell. There are three truncations, including a bitruncation
Truncated_120-cells
runcinated 120-cell (or runcinated 600-cell) is a convex uniform 4-polytope, being a runcination (a 3rd order truncation) of the regular 120-cell. There are
Runcinated_120-cells
Modern system for holding and firing missiles on naval vessels
launch system consists of a number of cells, which can hold one or more missiles ready for firing. Typically, each cell can hold a number of different types
Vertical_launching_system
cubical cells are connected to the other 24 cubical cells via all 6 square faces. The other 24 cubical cells are connected to the former 8 cells via only
Runcinated_tesseracts
Uniform 6-polytope
the 24-cell by a geometric folding of the E6/F4 Coxeter-Dynkin diagrams. This can be seen in the Coxeter plane projections. The 24 vertices of the 24-cell
2_21_polytope
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
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 Rectified 24-cell honeycomb Snub 24-cell honeycomb 5-cell honeycomb Truncated 5-cell honeycomb Omnitruncated 5-cell honeycomb
Runcinated_16-cell_honeycomb
Process by which cells are grown under controlled conditions
Cell culture or tissue culture is the process by which cells are grown under controlled conditions, generally outside of their natural environment. After
Cell_culture
South African mobile operator
Cell C, officially Cell C Limited, is a South African mobile telecoms operator headquartered in Sandton, Gauteng. As of 2026, it ranks as the fourth-largest
Cell_C
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
three 5-orthoplexes around each cell. It is dual to the 24-cell honeycomb honeycomb. Its vertex figure is the 16-cell honeycomb, {3,3,4,3}. List of regular
5-orthoplex_honeycomb
Geometric configuration of 12 points and 6 lines
of the 24-cell. Each central plane intersects 6 vertices in the form of a regular hexagon. Four hexagons intersect at each vertex of the 24-cell. The 12
Reye_configuration
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
Polygonal chain whose vertices are not all coplanar
This is 5 sides for a 5-cell, 8 sides for a tesseract and 16-cell, 12 sides for a 24-cell, and 30 sides for a 120-cell and 600-cell. When orthogonally projected
Skew_polygon
Stealth video game series
Tom Clancy's Splinter Cell is a series of action-adventure games, the first of which was released in 2002, and their tie-in novels that were endorsed by
Tom_Clancy's_Splinter_Cell
arrangement, and special characteristics. The same physically interchangeable cell size or battery size may have widely different characteristics; physical
List_of_battery_sizes
the rectified tesseract, rectified 8-cell is a uniform 4-polytope (4-dimensional polytope) bounded by 24 cells: 8 cuboctahedra, and 16 tetrahedra. It
Rectified_tesseract
Type of rechargeable battery without cobalt
battery with 1,000 km range". pv magazine International. Retrieved 2024-09-24. "Cell – CA Series". CALB.cn. Archived from the original on 2014-10-09. "A123
Lithium iron phosphate battery
Lithium_iron_phosphate_battery
Uniform 4-polytope bounded by 320 cells
on the top and bottom. (The snub 24-cell can also be constructed by another diminishing of the 600-cell, removing 24 icosahedral pyramids. Equivalently
Grand_antiprism
Isogonal polytope with regular facets
5-cell, snub 24-cell and rectified 600-cell. The only semiregular polytopes in higher dimensions are the k21 polytopes, where the rectified 5-cell is
Semiregular_polytope
Communications equipment location
A cell site, cell phone tower, cell base tower, or cellular base station is a cellular-enabled mobile device site where antennas and electronic communications
Cell_site
Carcinoma that derives from squamous epithelial cells
Squamous-cell carcinoma (SCC), also known as epidermoid carcinoma, comprises a number of different types of cancer that begin in squamous cells. These cells form
Squamous-cell_carcinoma
Object in 4-dimensional geometry
octahedral cupola can be sliced off from a runcinated 24-cell, on a hyperplane parallel to an octahedral cell. The cupola can be seen in a B2 and B3 Coxeter
Octahedral_cupola
Cell imaging
The cell painting assay is a high-content, high-throughput imaging technique used to capture a wide array of cellular phenotypes in response to diverse
Cell_painting
4D geometry item
geometry, a cantellated 120-cell is a convex uniform 4-polytope, being a cantellation (a 2nd order truncation) of the regular 120-cell. There are four degrees
Cantellated_120-cell
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
Place in prison housing inmates awaiting execution
the designated "death cell." To accommodate Zangara, the facility expanded the waiting area to include a row of adjacent cells, thus creating what became
Death_row
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
defines 2 types of 4-faces: rectified 5-cell, 021, and 24-cell, 0111. Removing a fourth end node defines 2 types of cells: octahedron, 011, and tetrahedron
2_22_honeycomb
Microfluidic cell culture integrates knowledge from biology, biochemistry, engineering, and physics to develop devices and techniques for culturing, maintaining
Microfluidic_cell_culture
Regular tiling of hyperbolic 3-space
It is analogous to the 24-cell and the 5-cell. A geometric honeycomb is a space-filling of polyhedral or higher-dimensional cells, so that there are no
Icosahedral_honeycomb
Unspecialized biological cell that can become specialized
multicellular organisms, stem cells are undifferentiated or partially differentiated cells that can change into various types of cells and proliferate indefinitely
Stem_cell
Type of pluripotent blastocystic stem cell
Embryonic stem cells (ESCs) are pluripotent stem cells derived from the inner cell mass of a blastocyst, an early-stage pre-implantation embryo. Human
Embryonic_stem_cell
Type of malignant cancer
Small-cell carcinoma is a type of highly aggressive cancer that most commonly arises within the lungs, but can also occasionally arise in the cervix, prostate
Small-cell_carcinoma
Multi-core microprocessor microarchitecture
The Cell Broadband Engine (Cell/B.E.) is a 64-bit reduced instruction set computer (RISC) multi-core processor and microarchitecture developed by Sony
Cell_(processor)
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
Steriruncic tesseractic honeycomb
Steriruncic_tesseractic_honeycomb
Geometric object
rectified 5-cell: 021, Tetroctahedric (5 tetrahedra and 5 octahedra cells) demipenteract: 121, 5-ic semiregular figure (16 5-cell and 10 16-cell facets) 2
Uniform_k_21_polytope
Uniform polytope
The complete family of 2k1 polytopes are: 5-cell: 201, (5 tetrahedra cells) Pentacross: 211, (32 5-cell (201) facets) 221, (72 5-simplex and 27 5-orthoplex
Uniform_2_k1_polytope
63rd Johnson solid (8 faces)
vertex figure of a snub 24-cell, a four-dimensional polytope consisting of 120 regular tetrahedra and 24 icosahedra as the cells. Augmented tridiminished
Tridiminished_icosahedron
Missile launching system
destroyer - (48 cells) Hunter-class frigate - (32 cells) Canada Iroquois-class destroyer - (29 cells) (Retired) River-class destroyer - (24 cells) Chile Adelaide-class
Mark 41 vertical launching system
Mark_41_vertical_launching_system
travel, tourism, insurance
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