# 正圖形列表

## 概觀

0 1 0 0 0 0 0 1
1 1 線段 0 1 0 0 0 1
2 正多邊形 星型多邊形 1 1 0 0
3 5 正多面體 4 Kepler–Poinsot solids 3 鑲嵌 0
4 6 四维凸正多胞体 10 Schläfli–Hess polychora 1 堆砌 4 0 11
5 3 五維凸正多胞體 0 3 四維堆砌 5 4 2
6 3 六維凸正多胞體 0 1 五維堆砌 0 0 5
7+ 3 0 1 0 0 0

## 二維正圖形

### 凸

(2-單體)
(equit)

(2-正軸形)
(2-立方形)
(square)

(pe)

(he)

(ha)

(oc)

(en)

(de)

#### 退化 (圓形)

名稱 施萊夫利符號 正一邊形 正二邊形 {1} {2}

#### 非凸

 名稱 施萊夫利符號 圖像 五角星 七角星 八角星 九角星 十角星 ...n角星 {5/2} (star) {7/2} (hag) {7/3} (gahg) {8/3} (og) {9/2} (eng) {9/4} (geng) {10/3} (dag) {p/q}

......

## 三維正圖形

### 凸

Name 施萊夫利符號
{p,q}

(透視圖)

(立體圖)

(球面投影)

{p}

{q}

(3-單體)
(三角錐)
(tet)
{3,3} 4
{3}
6 4
{3}
Td (自身對偶)

(3-立方形)
(正六面體)
(四角柱)
{4,3} 6
{4}
12 8
{3}
Oh 正八面體

(3-正軸體)
(反三稜柱)
(oct)
{3,4} 8
{3}
12 6
{4}
Oh 立方體

(doe)
{5,3} 12
{5}
30 20
{3}
Ih 正二十面體

(ike)
{3,5} 20
{3}
30 12
{5}
Ih 正十二面體

#### 退化 (球面)

In spherical geometry, the hosohedra {2,n}, dihedra {n,2} and henagonal henahedron {1,1} can be considered regular polyhedra (tilings of the sphere).

Some include:

Name Schläfli
{p,q}
Coxeter
diagram
Image
(sphere)
Faces
{p}
Edges Vertices
{q}
Symmetry Dual
Henagonal henahedron {1,1} 1
{1}
0 1
{1}
C1
(*1)
Self
Henagonal dihedron {1,2} 2
{1}
1 1
{2}
C1v
(*22)
Henagonal hosohedron
Henagonal hosohedron {2,1} 1
{2}
1 2
{1}
C1v
(*22)
Henagonal dihedron
Digonal dihedron
Digonal hosohedron
{2,2} 2
{2}
2 2
{2}
D2h
(*222)
Self
Trigonal hosohedron {2,3} 3
{2}
3 2
{3}
D3h
(*322)
Trigonal dihedron
Trigonal dihedron {3,2} 2
{3}
3 3
{2}
D3h
(*322)
Trigonal hosohedron
Hexagonal hosohedron {2,6} 6
{2}
6 2
{6}
D6h
(*622)
Hexagonal dihedron
Hexagonal dihedron {6,2} 2
{6}
6 6
{2}
D6h
(*622)
Hexagonal hosohedron

## 參考文獻

• Coxeter, Regular Polytopes, 3rd. ed., Dover Publications, 1973. ISBN 0-486-61480-8. (Tables I and II: Regular polytopes and honeycombs, pp. 294–296)
• Coxeter, The Beauty of Geometry: Twelve Essays, Dover Publications, 1999 ISBN 0-486-40919-8 (Chapter 10: Regular honeycombs in hyperbolic space, Summary tables II,III,IV,V, pp. 212–213) [1] PDF
• D. M. Y. Sommerville, An Introduction to the Geometry of n Dimensions. New York, E. P. Dutton, 1930. 196 pp. (Dover Publications edition, 1958) Chapter X: The Regular Polytopes