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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. [1]

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.

Apeirogon

In geometry, an apeirogon is a generalized polygon with a countably infinite number of sides.

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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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Cross-polytope

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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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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Dodecahedron

In geometry, a dodecahedron (Greek δωδεκάεδρον, from δώδεκα dōdeka "twelve" + ἕδρα hédra "base", "seat" or "face") is any polyhedron with twelve flat faces.

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Dual polyhedron

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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Edge (geometry)

In geometry, an edge is a particular type of line segment joining two vertices in a polygon, polyhedron, or higher-dimensional polytope.

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Egyptology

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.

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Euler characteristic

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.

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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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Flinders Petrie

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.

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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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Hemicube (geometry)

In abstract geometry, a hemi-cube is an abstract regular polyhedron, containing half the faces of a cube.

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Hexagonal tiling

In geometry, the hexagonal tiling or hexagonal tessellation is a regular tiling of the Euclidean plane, in which three hexagons meet at each vertex.

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Hypercube

In geometry, a hypercube is an n-dimensional analogue of a square (n.

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Icosahedron

In geometry, an icosahedron is a polyhedron with 20 faces.

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Octahedron

In geometry, an octahedron (plural: octahedra) is a polyhedron with eight faces.

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Order-4 hexagonal tiling

In geometry, the order-4 hexagonal tiling is a regular tiling of the hyperbolic plane.

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Order-7 triangular tiling

In geometry, the order-7 triangular tiling is a regular tiling of the hyperbolic plane with a Schläfli symbol of.

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Peter McMullen

Peter McMullen (born 11 May 1942) is a British mathematician, a professor emeritus of mathematics at University College London.

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Projection (linear algebra)

In linear algebra and functional analysis, a projection is a linear transformation P from a vector space to itself such that.

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Regular polygon

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).

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Regular polyhedron

A regular polyhedron is a polyhedron whose symmetry group acts transitively on its flags.

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Regular polytope

In mathematics, a regular polytope is a polytope whose symmetry is transitive on its flags, thus giving it the highest degree of symmetry.

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Regular Polytopes (book)

Regular Polytopes is a mathematical geometry book written by Canadian mathematician H.S.M. Coxeter.

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Semiregular polytope

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.

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Simple Lie group

In group theory, a simple Lie group is a connected non-abelian Lie group G which does not have nontrivial connected normal subgroups.

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Simplex

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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Skew polygon

In geometry, a skew polygon is a polygon whose vertices are not all coplanar.

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Surrey

Surrey is a county in the south east of England, one of the home counties bordering Greater London.

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Symmetry group

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.

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Tesseract

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.

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Tetrahedron

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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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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5-cell

In geometry, the 5-cell is a four-dimensional object bounded by 5 tetrahedral cells.

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600-cell

In geometry, the 600-cell is the convex regular 4-polytope (four-dimensional analogue of a Platonic solid) with Schläfli symbol.

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John Flinders Petrie, Petrial cube, Petrial dodecahedron, Petrial icosahedron, Petrial octahedron, Petrial tetrahedron, Petrie Polygon, Petrie dual.

References

[1] https://en.wikipedia.org/wiki/Petrie_polygon

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