In geometry , a 7-ORTHOPLEX, or 7-cross polytope , is a regular
It has two constructed forms, the first being regular with Schläfli
symbol {35,4}, and the second with alternately labeled
(checkerboarded) facets, with
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
ALTERNATE NAMES * HEPTACROSS, derived from combining the family name cross polytope
with hept for seven (dimensions) in Greek .
* HECATONICOSOCTAEXON as a 128-facetted
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 sy |