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The Info List - 7-orthoplex



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In geometry , a 7-ORTHOPLEX, or 7-cross polytope , is a regular 7-polytope
7-polytope
with 14 vertices , 84 edges , 280 triangle faces , 560 tetrahedron cells , 672 5-cells 4-faces, 448 5-faces, and 128 6-faces.

It has two constructed forms, the first being regular with Schläfli symbol {35,4}, and the second with alternately labeled (checkerboarded) facets, with Schläfli symbol
Schläfli symbol
{3,3,3,3,31,1} or Coxeter symbol 411.

It is a part of an infinite family of polytopes, called cross-polytopes or orthoplexes. The dual polytope is the 7-hypercube , or hepteract .

CONTENTS

* 1 Alternate names * 2 Images * 3 Construction * 4 Cartesian coordinates * 5 See also * 6 References * 7 External links

ALTERNATE NAMES

* HEPTACROSS, derived from combining the family name cross polytope with hept for seven (dimensions) in Greek . * HECATONICOSOCTAEXON as a 128-facetted 7-polytope
7-polytope
(polyexon).

IMAGES

orthographic projections COXETER PLANE B7 / A6 B6 / D7 B5 / D6 / A4

GRAPH

DIHEDRAL SYMMETRY

COXETER PLANE B4 / D5 B3 / D4 / A2 B2 / D3

GRAPH

DIHEDRAL SYMMETRY

COXETER PLANE A5 A3

GRAPH

DIHEDRAL SYMMETRY

CONSTRUCTION

There are two Coxeter groups associated with the 7-orthoplex, one regular , dual of the hepteract with the C7 or symmetry group, and a half symmetry with two copies of 6-simplex
6-simplex
facets, alternating,