38 relations: Angle trisection, Branko Grünbaum, Chaim Goodman-Strauss, Compass-and-straightedge construction, Constructible polygon, Coxeter element, Cyclic group, Digon, Dihedral group, Directed graph, E7 polytope, Enneagram (geometry), Euclidean tilings by convex regular polygons, Harold Scott MacDonald Coxeter, Hexagon, Internal and external angles, Isogonal figure, John Horton Conway, Neusis construction, Nonagon, Petrie polygon, Polygon, Projection (linear algebra), Regular polygon, Schläfli symbol, Simplex, Star polygon, Tomahawk (geometry), Truncated hexagonal tiling, Truncated trihexagonal tiling, Truncation (geometry), Zonogon, 1 32 polytope, 10-demicube, 10-orthoplex, 2 31 polytope, 9-cube, 9-orthoplex.
Angle trisection is a classical problem of compass and straightedge constructions of ancient Greek mathematics.
Branko Grünbaum (ברנקו גרונבאום; born 2 October 1929) is a Yugoslavian-born mathematician and a professor emeritus at the University of Washington in Seattle.
Chaim Goodman-Strauss (born June 1967 in Austin TX) is an American mathematician who works in convex geometry, especially aperiodic tiling.
Compass-and-straightedge construction, also known as ruler-and-compass construction or classical construction, is the construction of lengths, angles, and other geometric figures using only an idealized ruler and compass.
In mathematics, a constructible polygon is a regular polygon that can be constructed with compass and straightedge.
In mathematics, the Coxeter number h is the order of a Coxeter element of an irreducible Coxeter group.
In algebra, a cyclic group or monogenous group is a group that is generated by a single element.
In geometry, a digon is a polygon with two sides (edges) and two vertices.
In mathematics, a dihedral group is the group of symmetries of a regular polygon, which includes rotations and reflections.
In mathematics, and more specifically in graph theory, a directed graph (or digraph) is a graph that is a set of vertices connected by edges, where the edges have a direction associated with them.
In 7-dimensional geometry, there are 127 uniform polytopes with E7 symmetry.
In geometry, an enneagram is a nine-pointed plane figure.
Euclidean plane tilings by convex regular polygons have been widely used since antiquity.
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, an angle of a polygon is formed by two sides of the polygon that share an endpoint.
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.
John Horton Conway FRS (born 26 December 1937) is an English mathematician active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory.
The neusis is a geometric construction method that was used in antiquity by Greek mathematicians.
In geometry, a nonagon or enneagon is a nine-sided polygon or 9-gon.
In geometry, a Petrie polygon for a regular polytope of n dimensions is a skew polygon in which every (n – 1) consecutive sides (but no n) belongs to one of the facets.
In elementary geometry, a polygon is a plane figure that is bounded by a finite chain of straight line segments closing in a loop to form a closed polygonal chain or circuit.
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).
In geometry, the Schläfli symbol is a notation of the form that defines regular polytopes and tessellations.
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 star polygon is a type of non-convex polygon.
The tomahawk is a tool in geometry for angle trisection, the problem of splitting an angle into three equal parts.
In geometry, the truncated hexagonal tiling is a semiregular tiling of the Euclidean plane.
In geometry, the truncated trihexagonal tiling is one of eight semiregular tilings of the Euclidean plane.
In geometry, a truncation is an operation in any dimension that cuts polytope vertices, creating a new facet in place of each vertex.
In geometry, a zonogon is a centrally symmetric convex polygon.
In 7-dimensional geometry, 132 is a uniform polytope, constructed from the E7 group.
In geometry, a 10-demicube or demidekeract is a uniform 10-polytope, constructed from the 10-cube with alternated vertices removed.
In geometry, a 10-orthoplex or 10-cross polytope, is a regular 10-polytope with 20 vertices, 180 edges, 960 triangle faces, 3360 octahedron cells, 8064 5-cells 4-faces, 13440 5-faces, 15360 6-faces, 11520 7-faces, 5120 8-faces, and 1024 9-faces.
In 7-dimensional geometry, 231 is a uniform polytope, constructed from the E7 group.
In geometry, a 9-cube is a nine-dimensional hypercube with 512 vertices, 2304 edges, 4608 square faces, 5376 cubic cells, 4032 tesseract 4-faces, 2016 5-cube 5-faces, 672 6-cube 6-faces, 144 7-cube 7-faces, and 18 8-cube 8-faces.
In geometry, a 9-orthoplex or 9-cross polytope, is a regular 9-polytope with 18 vertices, 144 edges, 672 triangle faces, 2016 tetrahedron cells, 4032 5-cells 4-faces, 5376 5-simplex 5-faces, 4608 6-simplex 6-faces, 2304 7-simplex 7-faces, and 512 8-simplex 8-faces.