“Polytope families”的意思、由来-开放百科全书

词条

Polytope families

释义

There are several families of symmetric polytopes with irreducible symmetry which have a member in more than one dimensionality. These are tabulated here with Petrie polygon projection graphs and Coxeter-Dynkin diagrams.

Table of irreducible polytope families

Family
n

n-simplex

n-hypercube

n-orthoplex

n-demicube

1_k2

2_k1

k₂₁

pentagonal polytope

Group

A_n

B_n

I₂(p)

D_n

E₆

E₇

E₈

F₄

G₂

H_n

{{CDD|node_1|3|node}}Triangle

{{CDD|node_1|4|node}}Square

{{CDD|node_1|p|node}}
p-gon
(example: p=7)

{{CDD|node_1|6|node}}
Hexagon

{{CDD|node_1|5|node}}
Pentagon

{{CDD|node_1|3|node|3|node}}
Tetrahedron

{{CDD|node_1|4|node|3|node}}
Cube

{{CDD|node_1|3|node|4|node}}
Octahedron

{{CDD|nodea_1|3a|branch}}
Tetrahedron

{{CDD|node_1|5|node|3|node}}
Dodecahedron

{{CDD|node_1|3|node|5|node}}
Icosahedron

{{CDD|node_1|3|node|3|node|3|node}}
5-cell

{{CDD|node_1|4|node|3|node|3|node}}Tesseract

{{CDD|node_1|3|node|3|node|4|node}}
16-cell

{{CDD|nodea_1|3a|branch|3a|nodea}}Demitesseract

{{CDD|node_1|3|node|4|node|3|node}}
24-cell

{{CDD|node_1|5|node|3|node|3|node}}
120-cell

{{CDD|node_1|3|node|3|node|5|node}}
600-cell

{{CDD|node_1|3|node|3|node|3|node|3|node}}
5-simplex

{{CDD|node_1|4|node|3|node|3|node|3|node}}
5-cube

{{CDD|node_1|3|node|3|node|3|node|4|node}}
5-orthoplex

{{CDD|nodea_1|3a|branch|3a|nodea|3a|nodea}}
5-demicube

{{CDD|node_1|3|node|3|node|3|node|3|node|3|node}}
6-simplex

{{CDD|node_1|4|node|3|node|3|node|3|node|3|node}}
6-cube

{{CDD|node_1|3|node|3|node|3|node|3|node|4|node}}
6-orthoplex

{{CDD|nodea_1|3a|branch|3a|nodea|3a|nodea|3a|nodea}}
6-demicube

{{CDD|nodea|3a|nodea|3a|branch_01lr|3a|nodea|3a|nodea}}
1₂₂

{{CDD|nodea|3a|nodea|3a|branch|3a|nodea|3a|nodea_1}}
2₂₁

{{CDD|node_1|3|node|3|node|3|node|3|node|3|node|3|node}}
7-simplex

{{CDD|node_1|4|node|3|node|3|node|3|node|3|node|3|node}}
7-cube

{{CDD|node_1|3|node|3|node|3|node|3|node|3|node|4|node}}
7-orthoplex

{{CDD|nodea_1|3a|branch|3a|nodea|3a|nodea|3a|nodea|3a|nodea}}
7-demicube

{{CDD|nodea|3a|nodea|3a|nodea|3a|branch_01lr|3a|nodea|3a|nodea}}
1₃₂

{{CDD|nodea|3a|nodea|3a|nodea|3a|branch|3a|nodea|3a|nodea_1}}
2₃₁

{{CDD|nodea_1|3a|nodea|3a|nodea|3a|branch|3a|nodea|3a|nodea}}
3₂₁

{{CDD|node_1|3|node|3|node|3|node|3|node|3|node|3|node|3|node}}
8-simplex

{{CDD|node_1|4|node|3|node|3|node|3|node|3|node|3|node|3|node}}
8-cube

{{CDD|node_1|3|node|3|node|3|node|3|node|3|node|3|node|4|node}}
8-orthoplex

{{CDD|nodea_1|3a|branch|3a|nodea|3a|nodea|3a|nodea|3a|nodea|3a|nodea}}
8-demicube

{{CDD|nodea|3a|nodea|3a|nodea|3a|nodea|3a|branch_01lr|3a|nodea|3a|nodea}}
1₄₂

{{CDD|nodea|3a|nodea|3a|nodea|3a|nodea|3a|branch|3a|nodea|3a|nodea_1}}
2₄₁

{{CDD|nodea_1|3a|nodea|3a|nodea|3a|nodea|3a|branch|3a|nodea|3a|nodea}}
4₂₁

{{CDD|node_1|3|node|3|node|3|node|3|node|3|node|3|node|3|node|3|node}}
9-simplex

{{CDD|node_1|4|node|3|node|3|node|3|node|3|node|3|node|3|node|3|node}}
9-cube

{{CDD|node_1|3|node|3|node|3|node|3|node|3|node|3|node|3|node|4|node}}
9-orthoplex

{{CDD|nodea_1|3a|branch|3a|nodea|3a|nodea|3a|nodea|3a|nodea|3a|nodea|3a|nodea}}
9-demicube

{{CDD|node_1|3|node|3|node|3|node|3|node|3|node|3|node|3|node|3|node|3|node}}
10-simplex

{{CDD|node_1|4|node|3|node|3|node|3|node|3|node|3|node|3|node|3|node|3|node}}
10-cube

{{CDD|node_1|3|node|3|node|3|node|3|node|3|node|3|node|3|node|3|node|4|node}}
10-orthoplex

{{CDD|nodea_1|3a|branch|3a|nodea|3a|nodea|3a|nodea|3a|nodea|3a|nodea|3a|nodea|3a|nodea}}
10-demicube

2 : Polytopes|Multi-dimensional geometry

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