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The Info List - 7-cube



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(i) (i) (i) (i) (i)

6-faces 14 {4,34}

5-faces 84 {4,33}

4-faces 280 {4,3,3}

Cells 560 {4,3}

Faces 672 {4}

Edges 448

Vertices 128

Vertex figure
Vertex figure
6-simplex

Petrie polygon
Petrie polygon
tetradecagon

Coxeter group
Coxeter group
C7,

Dual 7-orthoplex
7-orthoplex

Properties convex

In geometry , a 7-CUBE is a seven-dimensional hypercube with 128 vertices , 448 edges , 672 square faces , 560 cubic cells , 280 tesseract 4-faces , 84 penteract 5-faces , and 14 hexeract 6-faces .

It can be named by its Schläfli symbol
Schläfli symbol
{4,35}, being composed of 3 6-cubes around each 5-face. It can be called a HEPTERACT, a portmanteau of tesseract (the 4-cube) and hepta for seven (dimensions) in Greek . It can also be called a regular TETRADECA-7-TOPE or TETRADECAEXON, being a 7 dimensional polytope constructed from 14 regular facets .

CONTENTS

* 1 Related polytopes * 2 Cartesian coordinates
Cartesian coordinates
* 3 Images * 4 Projections * 5 References * 6 External links

RELATED POLYTOPES

It is a part of an infinite family of polytopes, called hypercubes . The dual of a 7-cube
7-cube
is called a 7-orthoplex
7-orthoplex
, and is a part of the infinite family of cross-polytopes .

Applying an alternation operation, deleting alternating vertices of the hepteract, creates another uniform polytope , called a demihepteract , (part of an infinite family called demihypercubes ), which has 14 demihexeractic and 64 6-simplex 6-faces.

CARTESIAN COORDINATES

Cartesian coordinates
Cartesian coordinates
for the vertices of a hepteract centered at the origin and edge length 2 are (±1,±1,±1,±1,±1,±1,±1)

while the interior of the same consists of all points (x0, x1, x2, x3, x4, x5, x6) with -1 < xi < 1.

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

PROJECTIONS

This hypercube graph is an orthogonal projection . This orientation shows columns of vertices positioned a vertex-edge-vertex distance from one vertex on the left to one vertex on the right, and edges attaching adjacent columns of vertices. The number of vertices in each column represents rows in Pascal\'s triangle , being 1:7:21:35:35:21:7:1. Petri