50 relations: Apeirogon, Cambridge University Press, Coxeter element, Coxeter group, Cross-polytope, Cube, Decagram (geometry), Dodecahedron, Dual polyhedron, Edge (geometry), Egyptology, Face (geometry), Facet (geometry), Flinders Petrie, Geometry, Graph embedding, Great dodecahedron, Great icosahedron, Great stellated dodecahedron, Harold Scott MacDonald Coxeter, Hexagon, Hypercube, Icosahedron, Kepler–Poinsot polyhedron, London Mathematical Society, Octahedron, Order-7 triangular tiling, Patrick du Val, Peter McMullen, Petrie dual, Projection (linear algebra), Regular polygon, Regular polyhedron, Regular polytope, Regular Polytopes (book), Semiregular polytope, Simple Lie group, Simplex, Skew polygon, Small stellated dodecahedron, Symmetry group, Tesseract, Tetrahedron, The Fifty-Nine Icosahedra, University of Toronto, 120-cell, 16-cell, 24-cell, 5-cell, 600-cell.
In geometry, an apeirogon (from the Greek word ἄπειρος apeiros, "infinite, boundless" and γωνία gonia, "angle") is a generalized polygon with a countably infinite number of sides.
Cambridge University Press (CUP) is the publishing business of the University of Cambridge.
In mathematics, the Coxeter number h is the order of a Coxeter element of an irreducible 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).
In geometry, a cross-polytope, orthoplex, hyperoctahedron, or cocube is a regular, convex polytope that exists in n-dimensions.
In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex.
In geometry, a decagram is a 10-point star polygon.
In geometry, a dodecahedron (Greek δωδεκάεδρον, from δώδεκα dōdeka "twelve" + ἕδρα hédra "base", "seat" or "face") is any polyhedron with twelve flat faces.
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.
In geometry, an edge is a particular type of line segment joining two vertices in a polygon, polyhedron, or higher-dimensional polytope.
Egyptology (from Egypt and Greek -λογία, -logia. علم المصريات) is the study of ancient Egyptian history, language, literature, religion, architecture and art from the 5th millennium BC until the end of its native religious practices in the 4th century AD.
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.
In geometry, a facet is a feature of a polyhedron, polytope, or related geometric structure, generally of dimension one less than the structure itself.
Sir William Matthew Flinders Petrie, FRS, FBA (3 June 1853 – 28 July 1942), commonly known as Flinders Petrie, was an English Egyptologist and a pioneer of systematic methodology in archaeology and preservation of artifacts.
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.
In topological graph theory, an embedding (also spelled imbedding) of a graph G on a surface \Sigma is a representation of G on \Sigma in which points of \Sigma are associated with vertices and simple arcs (homeomorphic images of) are associated with edges in such a way that.
In geometry, the great dodecahedron is a Kepler–Poinsot polyhedron, with Schläfli symbol and Coxeter–Dynkin diagram of.
In geometry, the great icosahedron is one of four Kepler-Poinsot polyhedra (nonconvex regular polyhedra), with Schläfli symbol and Coxeter-Dynkin diagram of.
In geometry, the great stellated dodecahedron is a Kepler-Poinsot polyhedron, with Schläfli symbol.
Harold Scott MacDonald "Donald" Coxeter, FRS, FRSC, (February 9, 1907 – March 31, 2003) was a British-born Canadian geometer.
In geometry, a hexagon (from Greek ἕξ hex, "six" and γωνία, gonía, "corner, angle") is a six-sided polygon or 6-gon.
In geometry, a hypercube is an ''n''-dimensional analogue of a square and a cube.
In geometry, an icosahedron is a polyhedron with 20 faces.
In geometry, a Kepler–Poinsot polyhedron is any of four regular star polyhedra.
The London Mathematical Society (LMS) is one of the United Kingdom's learned societies for mathematics (the others being the Royal Statistical Society (RSS) and the Institute of Mathematics and its Applications (IMA)).
In geometry, an octahedron (plural: octahedra) is a polyhedron with eight faces, twelve edges, and six vertices.
In geometry, the order-7 triangular tiling is a regular tiling of the hyperbolic plane with a Schläfli symbol of.
Patrick du Val (March 26, 1903 – January 22, 1987) was a British mathematician, known for his work on algebraic geometry, differential geometry, and general relativity.
Peter McMullen (born 11 May 1942) is a British mathematician, a professor emeritus of mathematics at University College London.
In topological graph theory, the Petrie dual of a embedded graph (on a 2-manifold with all faces disks) is another embedded graph that has the Petrie polygons of the first embedding as its faces.
In linear algebra and functional analysis, a projection is a linear transformation P from a vector space to itself such that.
In Euclidean geometry, a regular polygon is a polygon that is equiangular (all angles are equal in measure) and equilateral (all sides have the same length).
A regular polyhedron is a polyhedron whose symmetry group acts transitively on its flags.
In mathematics, a regular polytope is a polytope whose symmetry group acts transitively on its flags, thus giving it the highest degree of symmetry.
Regular Polytopes is a mathematical geometry book written by Canadian mathematician Harold Scott MacDonald Coxeter.
In geometry, by Thorold Gosset's definition a semiregular polytope is usually taken to be a polytope that is vertex-uniform and has all its facets being regular polytopes.
In group theory, a simple Lie group is a connected non-abelian Lie group G which does not have nontrivial connected normal subgroups.
In geometry, a simplex (plural: simplexes or simplices) is a generalization of the notion of a triangle or tetrahedron to arbitrary dimensions.
In geometry, a skew polygon is a polygon whose vertices are not all coplanar.
In geometry, the small stellated dodecahedron is a Kepler-Poinsot polyhedron, named by Arthur Cayley, and with Schläfli symbol.
In group theory, the symmetry group of an object (image, signal, etc.) is the group of all transformations under which the object is invariant with composition as the group operation.
In geometry, the tesseract is the four-dimensional analogue of the cube; the tesseract is to the cube as the cube is to the square.
In geometry, a tetrahedron (plural: tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges, and four vertex corners.
The Fifty-Nine Icosahedra is a book written and illustrated by H. S. M. Coxeter, P. Du Val, H. T. Flather and J. F. Petrie.
The University of Toronto (U of T, UToronto, or Toronto) is a public research university in Toronto, Ontario, Canada on the grounds that surround Queen's Park.
In geometry, the 120-cell is the convex regular 4-polytope with Schläfli symbol.
In four-dimensional geometry, a 16-cell is a regular convex 4-polytope.
In geometry, the 24-cell is the convex regular 4-polytope (four-dimensional analogue of a Platonic solid) with Schläfli symbol.
In geometry, the 5-cell is a four-dimensional object bounded by 5 tetrahedral cells.
In geometry, the 600-cell is the convex regular 4-polytope (four-dimensional analogue of a Platonic solid) with Schläfli symbol.