# 正則地區圖

## 例子

χ g 施萊夫利符號 頂點 階數 備註
2 0 {p,2} p p 2 C2 × Dihp 4p Cp   多邊形二面體
2 0 {2,p} 2 p p C2 × Dihp 4p p-fold K2 多面形
2 0 {3,3} 4 6 4 S4 24 K4   正四面體
2 0 {4,3} 8 12 6 C2 × S4 48 K4 K2   立方體
2 0 {3,4} 6 12 8 C2 × S4 48 K2,2,2英语Turán graph   正八面體
2 0 {5,3} 20 30 12 C2 × A5 120   正十二面體
2 0 {3,5} 12 30 20 C2 × A5 120 K6 × K2   正二十面體
1 n1 {2p,2}/2 p p 1 Dih2p 4p Cp   多邊形二面體半形[9]
1 n1 {2,2p}/2 2 p p Dih2p 4p p-fold K2 多面形半形[9]
1 n1 {4,3}/2 4 6 3 S4 24 K4   立方體半形
1 n1 {3,4}/2 3 6 4 S4 24 2-fold K3 八面體半形
1 n1 {5,3}/2 10 15 6 A5 60 佩特森圖   十二面體半形
1 n1 {3,5}/2 6 15 10 A5 60 K6   二十面體半形

## 四維環形多面體

 {4,4}1,0(v:1, e:2, f:1) {4,4}1,1(v:2, e:4, f:2) {4,4}2,0(v:4, e:8, f:4) {4,4}2,1(v:5, e:10, f:5) {4,4}2,2(v:8, e:16, f:8) {3,6}1,0(v:1, e:3, f:2) {3,6}1,1(v:3, e:9, f:6) {3,6}2,0(v:4, e:12, f:8) {3,6}2,1(v:7, e:21, f:14) {3,6}2,2(v:12, e:36, f:24) {6,3}1,0(v:2, e:3, f:1) {6,3}1,1(v:6, e:9, f:3) {6,3}2,0(v:8, e:12, f:4) {6,3}2,1(v:14, e:21, f:7) {6,3}2,2(v:24, e:36, f:12)

## 參考文獻

1. ^ Conder, Marston; Dobcsányi, Peter, Determination of all regular maps of small genus, Journal of Combinatorial Theory, Series B, 2001, 81 (2): 224–242, doi:10.1006/jctb.2000.2008
2. Nedela, Roman, Maps, Hypermaps, and Related Topics (PDF), 2007 [2020-08-14], （原始内容存档 (PDF)于2016-03-04）.
3. van Wijk, Jarke J., Symmetric tiling of closed surfaces: visualization of regular maps (PDF), Proc. SIGGRAPH (ACM Transactions on Graphics), 2009, 28 (3): 12, doi:10.1145/1531326.1531355, （原始内容 (PDF)存档于2011-06-09）
4. ^ Marston D.E. Conder and Jicheng Ma. Regular maps with simple underlying graphs. Journal of Combinatorial Theory, Series B. 2015, 110: 1 – 18 [2020-08-14]. ISSN 0095-8956. doi:10.1016/j.jctb.2014.07.001. （原始内容存档于2020-08-24）.
5. ^ The hemicube. weddslist.com. [2020-08-14]. （原始内容存档于2019-05-02）.
6. ^ Gailiunas, Paul; 等. Polyhedral Models of the Projective Plane. Bridges 2018 Conference Proceedings (Tessellations Publishing). 2018: 543–546.
7. ^
8. Coxeter, H. S. M.; Moser, W. O. J., Generators and Relations for Discrete Groups, Ergebnisse der Mathematik und ihrer Grenzgebiete 14 4th, Springer Verlag, 1980, ISBN 978-0-387-09212-6
9. Séquin, Carlo. Symmetrical immersions of low-genus non-orientable regular maps (PDF). Berkeley University. [2020-08-14]. （原始内容存档 (PDF)于2015-09-23）.
10. ^ Coxeter 1980[8], 8.3 Maps of type {4,4} on a torus.
11. ^ Coxeter 1980[8], 8.4 Maps of type {3,6} or {6,3} on a torus.
12. ^ Schulte, Egon and Wills, Jörg M. On Coxeter's regular skew polyhedra. Discrete mathematics (Elsevier). 1986, 60: 253–262.