41 relations: Apeirogon, Coxeter element, Coxeter group, Cross-polytope, Cube, Dodecahedron, Dual polyhedron, Edge (geometry), Egyptology, Euler characteristic, Face (geometry), Facet (geometry), Flinders Petrie, Geometry, Harold Scott MacDonald Coxeter, Hemicube (geometry), Hexagonal tiling, Hypercube, Icosahedron, Octahedron, Order-4 hexagonal tiling, Order-7 triangular tiling, Peter McMullen, Projection (linear algebra), Regular polygon, Regular polyhedron, Regular polytope, Regular Polytopes (book), Semiregular polytope, Simple Lie group, Simplex, Skew polygon, Surrey, Symmetry group, Tesseract, Tetrahedron, 120-cell, 16-cell, 24-cell, 5-cell, 600-cell.
In geometry, an apeirogon is a generalized polygon with a countably infinite number of sides.
New!!: Petrie polygon and Apeirogon ·
In mathematics, the Coxeter number h is the order of a Coxeter element of an irreducible Coxeter group.
New!!: Petrie polygon and Coxeter element ·
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).
New!!: Petrie polygon and Coxeter group ·
In geometry, a cross-polytope, orthoplex, hyperoctahedron, or cocube is a regular, convex polytope that exists in any number of dimensions.
New!!: Petrie polygon and Cross-polytope ·
In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex.
New!!: Petrie polygon and Cube ·
In geometry, a dodecahedron (Greek δωδεκάεδρον, from δώδεκα dōdeka "twelve" + ἕδρα hédra "base", "seat" or "face") is any polyhedron with twelve flat faces.
New!!: Petrie polygon and Dodecahedron ·
In geometry, polyhedra are associated into pairs called duals, where the vertices of one correspond to the faces of the other.
New!!: Petrie polygon and Dual polyhedron ·
In geometry, an edge is a particular type of line segment joining two vertices in a polygon, polyhedron, or higher-dimensional polytope.
New!!: Petrie polygon and Edge (geometry) ·
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.
New!!: Petrie polygon and Egyptology ·
In mathematics, and more specifically in algebraic topology and polyhedral combinatorics, the Euler characteristic (or Euler number, or Euler–Poincaré characteristic) is a topological invariant, a number that describes a topological space's shape or structure regardless of the way it is bent.
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.
New!!: Petrie polygon and Face (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.
New!!: Petrie polygon and Facet (geometry) ·
Sir William Matthew Flinders Petrie, FRS (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.
New!!: Petrie polygon and Flinders Petrie ·
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.
New!!: Petrie polygon and Geometry ·
Harold Scott MacDonald "Donald" Coxeter, FRS, FRSC, (February 9, 1907 – March 31, 2003) was a British-born Canadian geometer.
In abstract geometry, a hemi-cube is an abstract regular polyhedron, containing half the faces of a cube.
In geometry, the hexagonal tiling or hexagonal tessellation is a regular tiling of the Euclidean plane, in which three hexagons meet at each vertex.
New!!: Petrie polygon and Hexagonal tiling ·
In geometry, a hypercube is an n-dimensional analogue of a square (n.
New!!: Petrie polygon and Hypercube ·
In geometry, an icosahedron is a polyhedron with 20 faces.
New!!: Petrie polygon and Icosahedron ·
In geometry, an octahedron (plural: octahedra) is a polyhedron with eight faces.
New!!: Petrie polygon and Octahedron ·
In geometry, the order-4 hexagonal tiling is a regular tiling of the hyperbolic plane.
In geometry, the order-7 triangular tiling is a regular tiling of the hyperbolic plane with a Schläfli symbol of.
Peter McMullen (born 11 May 1942) is a British mathematician, a professor emeritus of mathematics at University College London.
New!!: Petrie polygon and Peter McMullen ·
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).
New!!: Petrie polygon and Regular polygon ·
A regular polyhedron is a polyhedron whose symmetry group acts transitively on its flags.
In mathematics, a regular polytope is a polytope whose symmetry is transitive on its flags, thus giving it the highest degree of symmetry.
New!!: Petrie polygon and Regular polytope ·
Regular Polytopes is a mathematical geometry book written by Canadian mathematician H.S.M. 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.
New!!: Petrie polygon and Simple Lie group ·
In geometry, a simplex (plural: simplexes or simplices) is a generalization of the notion of a triangle or tetrahedron to arbitrary dimensions.
New!!: Petrie polygon and Simplex ·
In geometry, a skew polygon is a polygon whose vertices are not all coplanar.
New!!: Petrie polygon and Skew polygon ·
Surrey is a county in the south east of England, one of the home counties bordering Greater London.
New!!: Petrie polygon and Surrey ·
In abstract algebra, 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.
New!!: Petrie polygon and Symmetry group ·
In geometry, the tesseract is the four-dimensional analog of the cube; the tesseract is to the cube as the cube is to the square.
New!!: Petrie polygon and Tesseract ·
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.
New!!: Petrie polygon and Tetrahedron ·
In geometry, the 120-cell is the convex regular 4-polytope with Schläfli symbol.
New!!: Petrie polygon and 120-cell ·
In four-dimensional geometry, a 16-cell, is a regular convex 4-polytope.
New!!: Petrie polygon and 16-cell ·
In geometry, the 24-cell is the convex regular 4-polytope (four-dimensional analogue of a Platonic solid) with Schläfli symbol.
New!!: Petrie polygon and 24-cell ·
In geometry, the 5-cell is a four-dimensional object bounded by 5 tetrahedral cells.
New!!: Petrie polygon and 5-cell ·
In geometry, the 600-cell is the convex regular 4-polytope (four-dimensional analogue of a Platonic solid) with Schläfli symbol.
New!!: Petrie polygon and 600-cell ·