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Four-dimensional analog of the dodecahedron
In geometry, the 120-cell is the convex regular 4-polytope (four-dimensional analogue of a Platonic solid) with Schläfli symbol {5,3,3}. It is also called
120-cell
Four-dimensional analog of the icosahedron
five triangles meeting at every vertex. Its dual polytope is the 120-cell. The 600-cell is the fifth in the sequence of 6 convex regular 4-polytopes in
600-cell
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
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
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
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 geometry, a rectified 120-cell is a uniform 4-polytope formed as the rectification of the regular 120-cell. E. L. Elte identified it in 1912 as a semiregular
Rectified_120-cell
In geometry, the icosahedral 120-cell, polyicosahedron, faceted 600-cell or icosaplex is a regular star 4-polytope with Schläfli symbol {3,5,5/2}. It
Icosahedral_120-cell
5-dimensional regular honeycomb
120-cell honeycomb is one of five compact regular space-filling tessellations (or honeycombs). With Schläfli symbol {5,3,3,3}, it has three 120-cells
120-cell_honeycomb
Regular object in four dimensional geometry
content within the same radius. The 4-simplex (5-cell) is the limit smallest case, and the 120-cell is the largest. Complexity (as measured by comparing
24-cell
Four-dimensional geometric objects
there are 15 uniform polytopes with H4 symmetry. Two of these, the 120-cell and 600-cell, are regular. Each can be visualized as symmetric orthographic projections
H4_polytope
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 symmetric
List_of_regular_polytopes
stellated 120-cell, Great 120-cell, Grand 120-cell, Great stellated 120-cell, Grand stellated 120-cell, Great grand 120-cell, Great icosahedral 120-cell, Grand
List of polygons, polyhedra and polytopes
List_of_polygons,_polyhedra_and_polytopes
Icosahedral 120-cell Small stellated 120-cell Great 120-cell Grand 120-cell Great stellated 120-cell Grand stellated 120-cell Great grand 120-cell Great icosahedral
List_of_mathematical_shapes
In geometry, the great 120-cell or great polydodecahedron is a regular star 4-polytope with Schläfli symbol {5,5/2,5}. It is one of 10 regular Schläfli-Hess
Great_120-cell
Four-dimensional analogue of the tetrahedron
one: the 600-vertex 120-cell is a compound of 120 regular 5-cells. The 5-cell is self-dual, meaning its dual polytope is 5-cell itself. Its maximal intersection
5-cell
In geometry, the grand 120-cell or grand polydodecahedron is a regular star 4-polytope with Schläfli symbol {5,3,5/2}. It is one of 10 regular Schläfli-Hess
Grand_120-cell
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
Class of 4-dimensional polytopes
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}, 120-cell
Uniform_4-polytope
4-space, the great 120-cell honeycomb is one of four regular star-honeycombs. With Schläfli symbol {5,5/2,5,3}, it has three great 120-cells around each face
Great_120-cell_honeycomb
Type of regular star 4-polytope
In geometry, the great grand 120-cell or great grand polydodecahedron is a regular star 4-polytope with Schläfli symbol {5,5/2,3}. It is one of 10 regular
Great_grand_120-cell
Generalization of the Rubik's Cube in n-dimensions
shape: 120-cell (also called the hecatonicosachoron or dodecacontachoron) The 120-cell is a 4-D geometric figure (4-polytope) composed of 120 dodecahedra
N-dimensional sequential move puzzle
N-dimensional_sequential_move_puzzle
Regular Schläfli-Hess 4-polytope with 600 vertices
In geometry, the great grand stellated 120-cell or great grand stellated polydodecahedron is a regular star 4-polytope with Schläfli symbol {5/2,3,3},
Great grand stellated 120-cell
Great_grand_stellated_120-cell
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
Complicated polygon
In geometry, the small stellated 120-cell or stellated polydodecahedron is a regular star 4-polytope with Schläfli symbol {5/2,5,3}. It is one of 10 regular
Small_stellated_120-cell
Regular star 4-polytope with 600 faces
the figure regains regular faces. The Grand 600-cell is also dual to the great grand stellated 120-cell, mirroring the great icosahedron's duality with
Grand_600-cell
In geometry, the grand stellated 120-cell or grand stellated polydodecahedron is a regular star 4-polytope with Schläfli symbol {5/2,5,5/2}. It is one
Grand_stellated_120-cell
5-dimensional regular honeycomb
120-cell honeycomb is one of five compact regular space-filling tessellations (or honeycombs). With Schläfli symbol {5,3,3,5}, it has five 120-cells around
Order-5_120-cell_honeycomb
icosahedral 120-cell honeycomb is one of four regular star-honeycombs. With Schläfli symbol {3,5,5/2,5}, it has five icosahedral 120-cells around each
Order-5 icosahedral 120-cell honeycomb
Order-5_icosahedral_120-cell_honeycomb
stellated 120-cell honeycomb is one of four regular star-honeycombs. With Schläfli symbol {5/2,5,3,3}, it has three small stellated 120-cells around each
Small stellated 120-cell honeycomb
Small_stellated_120-cell_honeycomb
Geometric object with flat sides
In 4 dimensions, the 24-cell, with Schläfli symbol {3,4,3}. Also the great 120-cell {5,5/2,5} and grand stellated 120-cell {5/2,5,5/2}. Polygons and
Polytope
Natural number
120 (one hundred [and] twenty) is the natural number following 119 and preceding 121. In the Germanic languages, the number 120 was also formerly known
120_(number)
Regular star 4-polytope
In geometry, the great stellated 120-cell or great stellated polydodecahedron is a regular star 4-polytope with Schläfli symbol {5/2,3,5}. It is one of
Great_stellated_120-cell
Goldberg polyhedron with 42 faces
1) cell-centered orthogonal projection of the 120-cell It represents the exterior envelope of a cell-centered orthogonal projection of the 120-cell, one
Chamfered_dodecahedron
Polygon with 20 edges
Petrie polygon for the icosahedral 120-cell, small stellated 120-cell, great icosahedral 120-cell, and great grand 120-cell. Muriel Pritchett, University of
Icosagon
Four-dimensional geometric object with flat sides
content within the same radius. The 4-simplex (5-cell) is the limit smallest case, and the 120-cell is the largest. Complexity (as measured by comparing
4-polytope
Mathematical model of the physical space
of California Press. Stillwell, John (January 2001). "The Story of the 120-Cell" (PDF). Notices of the AMS. 48 (1): 17–25. Perez-Gracia, Alba; Thomas,
Euclidean_geometry
Polygon with 12 edges
24-cell, snub 24-cell, 6-6 duoprism, 6-6 duopyramid. In 6 dimensions 6-cube, 6-orthoplex, 221, 122. It is also the Petrie polygon for the grand 120-cell
Dodecagon
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
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
In geometry, the great icosahedral 120-cell, great polyicosahedron or great faceted 600-cell is a regular star 4-polytope with Schläfli symbol {3,5/2
Great_icosahedral_120-cell
Polyhedron associated with another by swapping vertices for faces
{3,3,...,3} The regular 24-cell in 4 dimensions, {3,4,3}. The great 120-cell {5,5/2,5} and the grand stellated 120-cell {5/2,5,5/2} The self-dual (infinite)
Dual_polyhedron
Regular polytope whose 2D form is a pentagon
pentagonal faces) 120-cell, {5, 3, 3} (120 dodecahedral cells) Order-3 120-cell honeycomb, {5, 3, 3, 3} (tessellates hyperbolic 4-space (∞ 120-cell facets) The
Pentagonal_polytope
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
Compound polyhedron
occur as cells of another regular 4-polytope inscribed within the 120-cell, the 600-cell, which has 600 regular tetrahedra as its cells. The 120-cell is a
Compound_of_five_tetrahedra
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
Isogonal polytope with uniform facets
[3,4,3]: the 24-cell {3,4,3}, self-dual; group [3,3,5]: 600-cell {3,3,5}, its dual 120-cell {5,3,3}, and their ten regular stellations. group [31,1,1]:
Uniform_polytope
Specific set of Hamiltonian quaternions with the same symmetry as the 600-cell
symmetry as the 600-cell. The term can be used to refer to two related, but distinct, concepts: The icosian group: a multiplicative group of 120 quaternions,
Icosian
120-cell honeycomb is one of five compact regular space-filling tessellations (or honeycombs). With Schläfli symbol {5,3,3,4}, it has four 120-cells around
Order-4_120-cell_honeycomb
icosahedral 120-cell honeycomb and great 120-cell honeycomb: the icosahedral 120-cells and great 120-cells in each honeycomb are replaced by the 600-cells that
Pentagrammic-order 600-cell honeycomb
Pentagrammic-order_600-cell_honeycomb
10-pointed star polygon
pentagram itself; the compound of two great 120-cells and the compound of two grand stellated 120-cells. A full list can be seen at Polytope compound#Compounds
Decagram_(geometry)
Set of points described by relative position in space
stellated 120-cell and great stellated 120-cell, both with pentagrammic faces, appear visually indistinguishable without a representation of their cells: George
Vertex_arrangement
480 edges. The snub 24-cell is a convex uniform 4-polytope that consists of 120 regular tetrahedra and 96 icosahedra as its cell, firstly described by
Dual_snub_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
Submarine class
(520 kW) each; 2 × Westinghouse Electric electric motors, 600 hp each; 1 × 120-cell Exide battery; 2 × propellers Speed: 15 kn (28 km/h; 17 mph) surfaced;
United States S-class submarine
United_States_S-class_submarine
N-dimensional polytope with vertices adjacent to N facets
regular 120-cell and tesseract. Simple uniform 4-polytope include the truncated 5-cell, truncated tesseract, truncated 24-cell, truncated 120-cell, and duoprisms
Simple_polytope
Australian mathematician
America's prestigious Chauvenet Prize for his article "The Story of the 120-Cell," Notices of the AMS, January 2001, pp. 17–24. In 2012, he became a fellow
John_Stillwell
Polygon with 30 edges
{30/7} is also the Petrie polygon for the great grand stellated 120-cell and grand 600-cell. Weisstein, Eric W. "Triacontagon". MathWorld. Constructible
Triacontagon
Fiber bundle of the 3-sphere over the 2-sphere, with 1-spheres as fibers
construction of the 120-cell By Gian Marco Todesco shows the Hopf fibration of the 120-cell. Video of one 30-cell ring of the 600-cell from http://page.math
Hopf_fibration
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
Prison on Côn Sơn Island, Vietnam
within which each cell occupies 1.408 m2, solariums occupy 1.873 m2, and other spaces occupy 2.194 m2. The prison includes 120 cells. The prison was closed
Côn_Đảo_Prison
Extending the elements of a polytope to form a new figure
example, in 4-space, the great grand stellated 120-cell is the final stellation of the regular 4-polytope 120-cell. The first systematic naming of stellated
Stellation
Shape with six sides
equilateral and equiangular. Its internal angle is one-third of a circle, equal to 120°. The Schläfli symbol denotes this polygon as { 6 } {\displaystyle \{6\}}
Hexagon
Plane figure bounded by line segments
honeycomb made by bees is an array of hexagons, and the sides and base of each cell are also polygons. In computer graphics, a polygon is a primitive used in
Polygon
Any of the five regular polyhedra
5-cell as {3,3,3}, 16-cell as {3,3,4}, 600-cell as {3,3,5}, tesseract as {4,3,3}, and 120-cell as {5,3,3}, and a sixth one, the self-dual 24-cell, {3
Platonic_solid
Royal Canadian Navy hunter-killer submarine
each driving a 1.4-megawatt (1,900 hp) GEC electric alternator with two 120-cell chloride batteries. The batteries have a 90-hour endurance at 3 knots (5
HMCS_Corner_Brook
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
Polyhedron with 12 faces
stellations of the convex form. All of these have icosahedral symmetry, order 120. Some dodecahedra have the same combinatorial structure as the regular dodecahedron
Dodecahedron
Perkel (1979). 11-cell – abstract regular polytope with hemi-icosahedral cells. 120-cell – regular 4-polytope with dodecahedral cells Order-5 dodecahedral
57-cell
5-dimensional hypercube
five-dimensional hypercube with 32 vertices, 80 edges, 80 square faces, 40 cubic cells, and 10 tesseract 4-faces. It is represented by Schläfli symbol {4,3,3,3}
5-cube
Puzzle
V-Cube 8 Pyraminx Skewb Diamond Tuttminx Dogic Combination puzzles Magic 120-cell "Megaminx". www.jaapsch.net. "TwistyPuzzles.com > Museum > Search". www
Megaminx
Branch of biology that studies cells
cells, with subtopics including the study of cell metabolism, cell communication, cell cycle, biochemistry, and cell composition. The study of cells is
Cell_biology
Submarine class
tests of the new combat system occurred on Tapajó in December 2011. Four 120-cell batteries are located forward and aft of the command center in the lower
Type_209_submarine
Compact regular space-filling tessellation
pente Its dual is the 120-cell honeycomb, {5,3,3,3}. It is related to the order-5 tesseractic honeycomb, {4,3,3,5}, and order-5 120-cell honeycomb, {5,3,3
Order-5_5-cell_honeycomb
Argentine submarine class
motor can propel it at speeds up to 25 knots (46 km/h; 29 mph). Eight 120-cell banks of VARTA batteries are installed on each boat. They have a diving
TR-1700-class_submarine
Oxygen-delivering blood cell and the most common type of blood cell
are produced per second in human adults. The cells develop in the bone marrow and circulate for about 100–120 days in the body before their components are
Red_blood_cell
Unfinished 1785 erotic novel by the Marquis de Sade
The 120 Days of Sodom, or the School of Libertinage (French: Les 120 Journées de Sodome ou l'école du libertinage) is an unfinished novel by the French
The_120_Days_of_Sodom
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
Solid with 12 equal pentagonal faces
of a dodecahedron. 120-cell, a regular polychoron (4D polytope whose surface consists of a hundred and twenty dodecahedral cells) Icosahedral twins -
Regular_dodecahedron
Shape with three equal sides
transformation and two rotations by the multiple of one-third of a full turn (0°, 120°, 240°). The inscribed circle of an equilateral triangle is a circle that
Equilateral_triangle
Group that admits a formal description in terms of reflections
dimensions, there are three exceptional regular polytopes, the 24-cell, the 120-cell, and the 600-cell. The first has symmetry group F4, while the other two are
Coxeter_group
Pentachoric group – A4, [3,3,3], (), order 120, (Du Val #51' (I†/C1;I/C1)†*, Conway +1/60[I×I].21), named for the 5-cell (pentachoron), given by ringed Coxeter
Point groups in four dimensions
Point_groups_in_four_dimensions
The list of human cell types provides an enumeration and description of the various specialized cells found within the human body, highlighting their
List_of_human_cell_types
Planar surface that forms part of the boundary of a solid object
4-dimensional tesseract has 24 square faces, each sharing two of 8 cubic cells. Any convex polyhedron's surface has Euler characteristic V − E + F = 2
Face_(geometry)
Multi-dimensional generalization of triangle
3-dimensional simplex is a tetrahedron, and a 4-dimensional simplex is a 5-cell. Specifically, a k-simplex is a k-dimensional polytope that is the convex
Simplex
{4,3,3,5}, it has five 8-cells (also known as tesseracts) around each face. Acronym: pitest Its dual is the order-4 120-cell honeycomb, {5,3,3,4}. It
Order-5_tesseractic_honeycomb
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
Rectified_24-cell
Uniform 4-polytope
tetrahedra. Its vertices are a subset of those of the small stellated 120-cell. The great duoantiprism can be constructed from a nonuniform variant of
Great_duoantiprism
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
Skew polygon derived from a polytope
three consecutive sides (but no four) belong to one of the polychoron's cells. As the surface of a 4-polytope is a 3-dimensional space (the 3-sphere)
Petrie_polygon
Topological invariant in mathematics
combinatorial cell complex, one defines the Euler characteristic as the number of 0-cells, minus the number of 1-cells, plus the number of 2-cells, etc., if
Euler_characteristic
Solid with twenty equal triangular faces
comparison mensuration. It is analogous to a four-dimensional polytope, the 600-cell. Regular icosahedra occur both in natural and human-made objects. A notable
Regular_icosahedron
6-dimensional hypercube
six-dimensional hypercube with 64 vertices, 192 edges, 240 square faces, 160 cubic cells, 60 tesseract 4-faces, and 12 5-cube 5-faces. It has Schläfli symbol {4
6-cube
Polytope in 8-dimensional geometry
421 polytope are projected into 4-space as two copies of the 120 vertices of the 600-cell, one copy smaller (scaled by the golden ratio) than the other
4_21_polytope
Irish mathematician (1860–1940)
roots of his proof. Stott created complete sets of models of the 120-cell and 600-cell, and left them with Schoute. The University of Groningen honoured
Alicia_Boole_Stott
a 120-cell, while the other shares the vertices of a 600-cell. It immediately follows therefore that the corresponding dual compounds of 75 16-cells are
List of regular polytope compounds
List_of_regular_polytope_compounds
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
Battery of statistical tests
in the weak inverse of the 120×120 covariance matrix yields a test equivalent to the likelihood ratio test that the 120 cell counts came from the specified
Diehard_tests
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)
Regular polytope dual to the hypercube in any number of dimensions
cross-polytope is a regular octahedron, and a 4-dimensional cross-polytope is a 16-cell. Its facets are simplexes of the previous dimension, while the cross-polytope's
Cross-polytope
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