46 relations: Cartesian coordinate system, Convex polytope, Coxeter group, Coxeter–Dynkin diagram, Cross-polytope, Dual polyhedron, Face (geometry), Four-dimensional space, Geometry, Harold Scott MacDonald Coxeter, Hyperplane, Hypersimplex, Isogonal figure, Isotoxal figure, John Horton Conway, Messenger of Mathematics, Michael Guy, Net (polyhedron), Norman Johnson (mathematician), Octahedron, Orthant, Pentagon, Petrie polygon, Platonic solid, Rectification (geometry), Rectified 5-cubes, Rectified 5-orthoplexes, Regular polytope, Schläfli symbol, Schlegel diagram, Simplex, Stereographic projection, Tetrahedron, Thorold Gosset, Triangle, Triangular bipyramid, Triangular prism, Truncated 5-cell, Uniform 4-polytope, Uniform k 21 polytope, Uniform polytope, Vertex figure, 2 21 polytope, 24-cell, 5-cell, 5-demicube.
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 from the point to two fixed perpendicular directed lines, measured in the same unit of length.
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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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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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).
In geometry, a cross-polytope, orthoplex, hyperoctahedron, or cocube is a regular, convex polytope that exists in any number of dimensions.
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In geometry, polyhedra are associated into pairs called duals, where the vertices of one correspond to the faces of the other.
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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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In mathematics, four-dimensional space ("4D") is a geometric space with four dimensions.
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 "Donald" Coxeter, FRS, FRSC, (February 9, 1907 – March 31, 2003) was a British-born Canadian geometer.
In geometry a hyperplane is a subspace of one dimension less than its ambient space.
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In polyhedral combinatorics, a hypersimplex, Δd,k, is a convex polytope that generalizes the simplex.
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In geometry, a polytope (a polygon, polyhedron or tiling, for example) is isogonal or vertex-transitive if, loosely speaking, all its vertices are the same.
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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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John Horton Conway FRS (born 26 December 1937) is a British mathematician active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory.
The Messenger of Mathematics is a defunct mathematics journal.
Michael J. T. Guy (born c.1942) is a British computer scientist and mathematician.
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In geometry the 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.
Norman W. Johnson (born November 12, 1930) is a mathematician, previously at Wheaton College, Norton, Massachusetts.
In geometry, an octahedron (plural: octahedra) is a polyhedron with eight faces.
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In geometry, an orthant or hyperoctant is the analogue in n-dimensional Euclidean space of a quadrant in the plane or an octant in three dimensions.
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In geometry, a pentagon (from the Greek πέντε pente and γωνία gonia, meaning five and angle) is any five-sided polygon.
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In geometry, a Petrie polygon for a regular polytope of n dimensions is a skew polygon such that every (n-1) consecutive sides (but no n) belong to one of the facets.
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In three-dimensional space, a Platonic solid is a regular, convex polyhedron.
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In Euclidean geometry, rectification or complete-truncation is the process of truncating a polytope by marking the midpoints of all its edges, and cutting off its vertices at those points.
In five-dimensional geometry, a rectified 5-cube is a convex uniform 5-polytope, being a rectification of the regular 5-cube.
In five-dimensional geometry, a rectified 5-orthoplex is a convex uniform 5-polytope, being a rectification of the regular 5-orthoplex.
In mathematics, a regular polytope is a polytope whose symmetry is transitive on its flags, thus giving it the highest degree of symmetry.
In geometry, the Schläfli symbol is a notation of the form that defines regular polytopes and tessellations.
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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.
In geometry, a simplex (plural: simplexes or simplices) is a generalization of the notion of a triangle or tetrahedron to arbitrary dimensions.
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In geometry, the stereographic projection is a particular mapping (function) that projects a sphere onto a plane.
In geometry, a tetrahedron (plural: tetrahedra or tetrahedrons) is a polyhedron composed of four triangular faces, three of which meet at each corner or vertex.
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John Herbert de Paz Thorold Gosset (16 October 1869 – December 1962) was an English lawyer and an amateur mathematician.
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A triangle is a polygon with three edges and three vertices.
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In geometry, the triangular bipyramid (or dipyramid) is a type of hexahedron, being the first in the infinite set of face-transitive bipyramids.
In geometry, a triangular prism is a three-sided prism; it is a polyhedron made of a triangular base, a translated copy, and 3 faces joining corresponding sides.
In geometry, a truncated 5-cell is a uniform 4-polytope (4-dimensional uniform polytope) formed as the truncation of the regular 5-cell.
In geometry, a uniform 4-polytope is a 4-polytope which is vertex-transitive and whose cells are uniform polyhedra, and faces are regular polygons.
In geometry, a uniform k21 polytope is a polytope in k + 4 dimensions constructed from the ''E''''n'' Coxeter group, and having only regular polytope facets.
A uniform polytope of dimension three or higher is a vertex-transitive polytope bounded by uniform facets.
In geometry a vertex figure is, broadly speaking, the figure exposed when a corner of a polyhedron or polytope is sliced off.
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In 6-dimensional geometry, the 221 polytope is a uniform 6-polytope, constructed within the symmetry of the E6 group.
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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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In geometry, the 5-cell is a four-dimensional object bounded by 5 tetrahedral cells.
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In five-dimensional geometry, a demipenteract or 5-demicube is a semiregular 5-polytope, constructed from a 5-hypercube (penteract) with alternated vertices truncated.
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