Demiocteract - Citizendia

Demiocteract 8-demicube
(No image)
Type	Uniform 8-polytope
Family	demihypercube
7-faces	144: 16 demihepteracts 128 7-simplices
6-faces	112 demihexeracts 1024 6-simplices
5-faces	448 demipenteracts 3584 5-simplices
4-faces	1120 16-cells 7168 5-cells
Cells	10752: 1792+8960 {3,3}
Faces	7168 {3}
Edges	1792
Vertices	128
Vertex figure	Rectified 7-simplex
Schläfli symbol	t₀{3^1,1,5} h{4,3,3,3,3,3,3}
Coxeter-Dynkin diagram
Symmetry group	B₈, [3,3,3,3,3,3,4]
Dual	?
Properties	convex

A demiocteract is a uniform 8-polytope, constructed from the 8-hypercube, octeract, with alternated vertices deleted. In Geometry, demihypercubes (also called n-demicubes, n-hemicubes, and half measure polytopes) are a class of n- Polytopes constructed Regular and uniform 8-polytopes by fundamental Coxeter groups Regular polyzetta can be represented by the Schläfli symbol {pqrstuv} with v {pqrstu} In Geometry, demihypercubes (also called n-demicubes, n-hemicubes, and half measure polytopes) are a class of n- Polytopes constructed See also 7-polytope Demihypercube See also Other regular 7-polytopes Hepteract - {4333333} Heptacross - {3333334} See also 6-polytope Demihypercube See also Other regular 6-polytopes Hexeract - {433333} Hexacross - {333334} Cartesian coordinates Cartesian coordinates for the vertices of a demipenteract centered at the origin and edge length 2√2 are alternate halves of the Penteract Cartesian coordinates The hexateron can be constructed from a Pentachoron (4-simplex by adding a 6th vertex suchthat it is equidistant with all the other vertices Geometry The pentachoron is self- dual, and its Vertex figure is a tetrahedron A tetrahedron (plural tetrahedra) is a Polyhedron composed of four triangular faces three of which meet at each vertex. A triangle is one of the basic Shapes of Geometry: a Polygon with three corners or vertices and three sides or edges which are Line In Geometry a vertex figure is broadly speaking the figure exposed when a corner of a Polyhedron or Polytope is sliced off In Mathematics, the Schläfli symbol is a notation of the form {pqr In Mathematics, a Coxeter group, named after HSM Coxeter, is an abstract group that admits a formal description in terms of mirror symmetries In Euclidean space, an object is convex if for every pair of points within the object every point on the Straight line segment that joins them is also within the Regular and uniform 8-polytopes by fundamental Coxeter groups Regular polyzetta can be represented by the Schläfli symbol {pqrstuv} with v {pqrstu} In Geometry, a hypercube is an n -dimensional analogue of a square ( n = 2 and a Cube ( n = 3 Cartesian coordinates Cartesian coordinates for the vertices of a penteract centered at the origin and edge length 2 are (±1±1±1±1±1±1±1±1 It is part of a dimensionally infinite family of uniform polytopes called demihypercubes. A uniform polytope is a Vertex-transitive Polytope made from uniform polytope facets. In Geometry, demihypercubes (also called n-demicubes, n-hemicubes, and half measure polytopes) are a class of n- Polytopes constructed

Coxeter named this polytope as 1₅₁ from its Coxeter-Dynkin diagram, with a ring on one of the 1-length Coxeter-Dynkin diagram branches. Harold Scott MacDonald "Donald" Coxeter CC ( February 9, 1907 – March 31, 2003) is regarded as one of the great

External links

Olshevsky, George, Demiocteract at Glossary for Hyperspace. Regular and uniform 8-polytopes by fundamental Coxeter groups Regular polyzetta can be represented by the Schläfli symbol {pqrstuv} with v {pqrstu} George Olshevsky (born 1946 is a freelance editor, Writer, Publisher, Paleontologist, and Mathematician living in San Diego
Multi-dimensional Glossary

© 2009 citizendia.org; parts available under the terms of GNU Free Documentation License, from http://en.wikipedia.org
network: | |