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65 relations: Automorphism, Binary icosahedral group, Binary octahedral group, Binary tetrahedral group, Bitruncation, Cantellated 24-cells, Cartesian coordinate system, Commutator subgroup, Configuration (polytope), Convex hull, Convex polytope, Coxeter element, Coxeter group, Coxeter notation, Coxeter–Dynkin diagram, Cube, Demihypercube, Dicyclic group, Disphenoid, Dual polyhedron, Emanuel Lodewijk Elte, F4 (mathematics), Face (geometry), Facet (geometry), Geometry, Harold Scott MacDonald Coxeter, Hexagon, Hurwitz quaternion, Isogonal figure, Isohedral figure, Isosceles triangle, Isotoxal figure, Minkowski addition, Net (polyhedron), Norman Johnson (mathematician), Octagon, Omnitruncation, Perspective (graphical), Polyhedral combinatorics, Polytope, Rectified 24-cell, Regular skew polyhedron, Root system, Runcinated 24-cells, Schläfli symbol, Schlegel diagram, Square, Stereographic projection, Triakis octahedron, Triangle, ..., Truncated 24-cells, Truncated cube, Truncated cuboctahedron, Truncated octahedron, Truncated tetrahedron, Truncation (geometry), Uniform 4-polytope, Vertex figure, Wythoff construction, Zonohedron, 120-cell, 16-cell, 24-cell, 3-sphere, 4-polytope. Expand index (15 more) »
Automorphism
In mathematics, an automorphism is an isomorphism from a mathematical object to itself.
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Binary icosahedral group
In mathematics, the binary icosahedral group 2I or is a certain nonabelian group of order 120.
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Binary octahedral group
In mathematics, the binary octahedral group, name as 2O or is a certain nonabelian group of order 48.
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Binary tetrahedral group
In mathematics, the binary tetrahedral group, denoted 2T or 2,3,3 is a certain nonabelian group of order 24.
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Bitruncation
In geometry, a bitruncation is an operation on regular polytopes.
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Cantellated 24-cells
In four-dimensional geometry, a cantellated 24-cell is a convex uniform 4-polytope, being a cantellation (a 2nd order truncation) of the regular 24-cell.
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Cartesian coordinate system
A Cartesian coordinate system is a coordinate system that specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular directed lines, measured in the same unit of length.
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Commutator subgroup
In mathematics, more specifically in abstract algebra, the commutator subgroup or derived subgroup of a group is the subgroup generated by all the commutators of the group.
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Configuration (polytope)
In geometry, H. S. M. Coxeter called a regular polytope a special kind of configuration.
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Convex hull
In mathematics, the convex hull or convex envelope or convex closure of a set X of points in the Euclidean plane or in a Euclidean space (or, more generally, in an affine space over the reals) is the smallest convex set that contains X. For instance, when X is a bounded subset of the plane, the convex hull may be visualized as the shape enclosed by a rubber band stretched around X., p. 3.
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Convex polytope
A convex polytope is a special case of a polytope, having the additional property that it is also a convex set of points in the n-dimensional space Rn.
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Coxeter element
In mathematics, the Coxeter number h is the order of a Coxeter element of an irreducible Coxeter group.
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Coxeter group
In mathematics, a Coxeter group, named after H. S. M. Coxeter, is an abstract group that admits a formal description in terms of reflections (or kaleidoscopic mirrors).
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Coxeter notation
In geometry, Coxeter notation (also Coxeter symbol) is a system of classifying symmetry groups, describing the angles between with fundamental reflections of a Coxeter group in a bracketed notation expressing the structure of a Coxeter-Dynkin diagram, with modifiers to indicate certain subgroups.
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Coxeter–Dynkin diagram
In geometry, a Coxeter–Dynkin diagram (or Coxeter diagram, Coxeter graph) is a graph with numerically labeled edges (called branches) representing the spatial relations between a collection of mirrors (or reflecting hyperplanes).
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Cube
In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex.
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Demihypercube
In geometry, demihypercubes (also called n-demicubes, n-hemicubes, and half measure polytopes) are a class of n-polytopes constructed from alternation of an n-hypercube, labeled as hγn for being half of the hypercube family, γn.
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Dicyclic group
In group theory, a dicyclic group (notation Dicn or Q4n) is a member of a class of non-abelian groups of order 4n (n > 1).
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Disphenoid
In geometry, a disphenoid (from Greek sphenoeides, "wedgelike") is a tetrahedron whose four faces are congruent acute-angled triangles.
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Dual polyhedron
In geometry, any polyhedron is associated with a second dual figure, where the vertices of one correspond to the faces of the other and the edges between pairs of vertices of one correspond to the edges between pairs of faces of the other.
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Emanuel Lodewijk Elte
Emanuel Lodewijk Elte (16 March 1881 in Amsterdam – 9 April 1943 in Sobibór) at joodsmonument.nl was a Dutch mathematician.
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F4 (mathematics)
In mathematics, F4 is the name of a Lie group and also its Lie algebra f4.
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Face (geometry)
In solid geometry, a face is a flat (planar) surface that forms part of the boundary of a solid object; a three-dimensional solid bounded exclusively by flat faces is a polyhedron.
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Facet (geometry)
In geometry, a facet is a feature of a polyhedron, polytope, or related geometric structure, generally of dimension one less than the structure itself.
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Geometry
Geometry (from the γεωμετρία; geo- "earth", -metron "measurement") is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space.
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Harold Scott MacDonald Coxeter
Harold Scott MacDonald "Donald" Coxeter, FRS, FRSC, (February 9, 1907 – March 31, 2003) was a British-born Canadian geometer.
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Hexagon
In geometry, a hexagon (from Greek ἕξ hex, "six" and γωνία, gonía, "corner, angle") is a six-sided polygon or 6-gon.
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Hurwitz quaternion
In mathematics, a Hurwitz quaternion (or Hurwitz integer) is a quaternion whose components are either all integers or all half-integers (halves of an odd integer; a mixture of integers and half-integers is excluded).
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Isogonal figure
In geometry, a polytope (a polygon, polyhedron or tiling, for example) is isogonal or vertex-transitive if all its vertices are equivalent under the symmetries of the figure.
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Isohedral figure
In geometry, a polytope of dimension 3 (a polyhedron) or higher is isohedral or face-transitive when all its faces are the same.
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Isosceles triangle
In geometry, an isosceles triangle is a triangle that has two sides of equal length.
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Isotoxal figure
In geometry, a polytope (for example, a polygon or a polyhedron), or a tiling, is isotoxal or edge-transitive if its symmetries act transitively on its edges.
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Minkowski addition
In geometry, the Minkowski sum (also known as dilation) of two sets of position vectors A and B in Euclidean space is formed by adding each vector in A to each vector in B, i.e., the set Analogously, the Minkowski difference (or geometric difference) is defined as It is important to note that in general A - B\ne A+(-B).
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Net (polyhedron)
In geometry a net of a polyhedron is an arrangement of edge-joined polygons in the plane which can be folded (along edges) to become the faces of the polyhedron.
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Norman Johnson (mathematician)
Norman Woodason Johnson (November 12, 1930 – July 13, 2017) was a mathematician, previously at Wheaton College, Norton, Massachusetts.
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Octagon
In geometry, an octagon (from the Greek ὀκτάγωνον oktágōnon, "eight angles") is an eight-sided polygon or 8-gon.
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Omnitruncation
In geometry, an omnitruncation is an operation applied to a regular polytope (or honeycomb) in a Wythoff construction that creates a maximum number of facets.
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Perspective (graphical)
Perspective (from perspicere "to see through") in the graphic arts is an approximate representation, generally on a flat surface (such as paper), of an image as it is seen by the eye.
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Polyhedral combinatorics
Polyhedral combinatorics is a branch of mathematics, within combinatorics and discrete geometry, that studies the problems of counting and describing the faces of convex polyhedra and higher-dimensional convex polytopes.
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Polytope
In elementary geometry, a polytope is a geometric object with "flat" sides.
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Rectified 24-cell
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: 24 cubes, and 24 cuboctahedra.
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Regular skew polyhedron
In geometry, the regular skew polyhedra are generalizations to the set of regular polyhedron which include the possibility of nonplanar faces or vertex figures.
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Root system
In mathematics, a root system is a configuration of vectors in a Euclidean space satisfying certain geometrical properties.
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Runcinated 24-cells
In four-dimensional geometry, a runcinated 24-cell is a convex uniform 4-polytope, being a runcination (a 3rd order truncation) of the regular 24-cell.
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Schläfli symbol
In geometry, the Schläfli symbol is a notation of the form that defines regular polytopes and tessellations.
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Schlegel diagram
In geometry, a Schlegel diagram is a projection of a polytope from R^d into R^ through a point beyond one of its facets or faces.
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Square
In geometry, a square is a regular quadrilateral, which means that it has four equal sides and four equal angles (90-degree angles, or (100-gradian angles or right angles). It can also be defined as a rectangle in which two adjacent sides have equal length. A square with vertices ABCD would be denoted.
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Stereographic projection
In geometry, the stereographic projection is a particular mapping (function) that projects a sphere onto a plane.
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Triakis octahedron
In geometry, a triakis octahedron (or trigonal trisoctahedron or kisoctahedron) is an Archimedean dual solid, or a Catalan solid.
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Triangle
A triangle is a polygon with three edges and three vertices.
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Truncated 24-cells
In geometry, a truncated 24-cell is a uniform 4-polytope (4-dimensional uniform polytope) formed as the truncation of the regular 24-cell.
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Truncated cube
In geometry, the truncated cube, or truncated hexahedron, is an Archimedean solid.
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Truncated cuboctahedron
In geometry, the truncated cuboctahedron is an Archimedean solid, named by Kepler as a truncation of a cuboctahedron.
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Truncated octahedron
In geometry, the truncated octahedron is an Archimedean solid.
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Truncated tetrahedron
In geometry, the truncated tetrahedron is an Archimedean solid.
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Truncation (geometry)
In geometry, a truncation is an operation in any dimension that cuts polytope vertices, creating a new facet in place of each vertex.
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Uniform 4-polytope
In geometry, a uniform 4-polytope (or uniform polychoron) is a 4-polytope which is vertex-transitive and whose cells are uniform polyhedra, and faces are regular polygons.
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Vertex figure
In geometry, a vertex figure, broadly speaking, is the figure exposed when a corner of a polyhedron or polytope is sliced off.
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Wythoff construction
In geometry, a Wythoff construction, named after mathematician Willem Abraham Wythoff, is a method for constructing a uniform polyhedron or plane tiling.
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Zonohedron
A zonohedron is a convex polyhedron with point symmetry, every face of which is a polygon with point symmetry.
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120-cell
In geometry, the 120-cell is the convex regular 4-polytope with Schläfli symbol.
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16-cell
In four-dimensional geometry, a 16-cell is a regular convex 4-polytope.
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24-cell
In geometry, the 24-cell is the convex regular 4-polytope (four-dimensional analogue of a Platonic solid) with Schläfli symbol.
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3-sphere
In mathematics, a 3-sphere, or glome, is a higher-dimensional analogue of a sphere.
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4-polytope
In geometry, a 4-polytope (sometimes also called a polychoron, polycell, or polyhedroid) is a four-dimensional polytope.
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Redirects here:
288-cell, 48-cell, Bitruncated 24-cell, Cantitruncated 16-cell, Disphenoidal 288-cell, Omnitruncated demitesseract, Tetracontaoctachoron, Tetracontoctachoron, Truncated 24-cell, Truncated icositetrachoron.
References
[1] https://en.wikipedia.org/wiki/Truncated_24-cells
