Polytope of Type {24}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24}*48
Also Known As : 24-gon, {24}. if this polytope has another name.
Group : SmallGroup(48,7)
Rank : 2
Schlafli Type : {24}
Number of vertices, edges, etc : 24, 24
Order of s0s1 : 24
Special Properties :
Universal
Spherical
Locally Spherical
Orientable
Self-Dual
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{24,2} of size 96
{24,4} of size 192
{24,4} of size 192
{24,4} of size 192
{24,4} of size 192
{24,6} of size 288
{24,6} of size 288
{24,6} of size 288
{24,3} of size 288
{24,4} of size 384
{24,8} of size 384
{24,8} of size 384
{24,8} of size 384
{24,8} of size 384
{24,4} of size 384
{24,4} of size 384
{24,4} of size 384
{24,6} of size 384
{24,4} of size 384
{24,4} of size 384
{24,6} of size 384
{24,10} of size 480
{24,12} of size 576
{24,12} of size 576
{24,12} of size 576
{24,12} of size 576
{24,12} of size 576
{24,12} of size 576
{24,3} of size 576
{24,6} of size 576
{24,4} of size 576
{24,4} of size 576
{24,6} of size 576
{24,6} of size 576
{24,6} of size 576
{24,6} of size 576
{24,14} of size 672
{24,8} of size 768
{24,8} of size 768
{24,4} of size 768
{24,8} of size 768
{24,8} of size 768
{24,16} of size 768
{24,16} of size 768
{24,16} of size 768
{24,16} of size 768
{24,16} of size 768
{24,16} of size 768
{24,4} of size 768
{24,8} of size 768
{24,4} of size 768
{24,4} of size 768
{24,8} of size 768
{24,8} of size 768
{24,8} of size 768
{24,4} of size 768
{24,4} of size 768
{24,3} of size 768
{24,4} of size 768
{24,4} of size 768
{24,8} of size 768
{24,8} of size 768
{24,8} of size 768
{24,8} of size 768
{24,6} of size 768
{24,8} of size 768
{24,8} of size 768
{24,12} of size 768
{24,8} of size 768
{24,8} of size 768
{24,12} of size 768
{24,4} of size 768
{24,4} of size 768
{24,12} of size 768
{24,4} of size 768
{24,12} of size 768
{24,12} of size 768
{24,4} of size 768
{24,12} of size 768
{24,18} of size 864
{24,6} of size 864
{24,6} of size 864
{24,18} of size 864
{24,6} of size 864
{24,9} of size 864
{24,3} of size 864
{24,6} of size 864
{24,6} of size 864
{24,6} of size 864
{24,6} of size 864
{24,6} of size 864
{24,20} of size 960
{24,20} of size 960
{24,6} of size 960
{24,6} of size 960
{24,10} of size 960
{24,10} of size 960
{24,4} of size 960
{24,4} of size 960
{24,6} of size 960
{24,6} of size 960
{24,10} of size 960
{24,10} of size 960
{24,22} of size 1056
{24,12} of size 1152
{24,12} of size 1152
{24,12} of size 1152
{24,4} of size 1152
{24,24} of size 1152
{24,24} of size 1152
{24,24} of size 1152
{24,24} of size 1152
{24,24} of size 1152
{24,24} of size 1152
{24,24} of size 1152
{24,24} of size 1152
{24,24} of size 1152
{24,8} of size 1152
{24,8} of size 1152
{24,8} of size 1152
{24,24} of size 1152
{24,24} of size 1152
{24,24} of size 1152
{24,8} of size 1152
{24,12} of size 1152
{24,12} of size 1152
{24,12} of size 1152
{24,4} of size 1152
{24,3} of size 1152
{24,6} of size 1152
{24,12} of size 1152
{24,12} of size 1152
{24,6} of size 1152
{24,6} of size 1152
{24,12} of size 1152
{24,12} of size 1152
{24,12} of size 1152
{24,12} of size 1152
{24,12} of size 1152
{24,6} of size 1152
{24,12} of size 1152
{24,6} of size 1152
{24,6} of size 1152
{24,12} of size 1152
{24,12} of size 1152
{24,12} of size 1152
{24,12} of size 1152
{24,6} of size 1152
{24,6} of size 1152
{24,6} of size 1152
{24,12} of size 1152
{24,12} of size 1152
{24,6} of size 1152
{24,6} of size 1152
{24,6} of size 1152
{24,12} of size 1152
{24,12} of size 1152
{24,12} of size 1152
{24,6} of size 1152
{24,12} of size 1152
{24,3} of size 1152
{24,12} of size 1152
{24,12} of size 1152
{24,3} of size 1152
{24,26} of size 1248
{24,28} of size 1344
{24,28} of size 1344
{24,30} of size 1440
{24,30} of size 1440
{24,30} of size 1440
{24,6} of size 1440
{24,6} of size 1440
{24,15} of size 1440
{24,34} of size 1632
{24,36} of size 1728
{24,12} of size 1728
{24,36} of size 1728
{24,12} of size 1728
{24,36} of size 1728
{24,12} of size 1728
{24,12} of size 1728
{24,36} of size 1728
{24,12} of size 1728
{24,12} of size 1728
{24,9} of size 1728
{24,18} of size 1728
{24,3} of size 1728
{24,6} of size 1728
{24,12} of size 1728
{24,12} of size 1728
{24,4} of size 1728
{24,4} of size 1728
{24,12} of size 1728
{24,12} of size 1728
{24,4} of size 1728
{24,4} of size 1728
{24,12} of size 1728
{24,12} of size 1728
{24,12} of size 1728
{24,12} of size 1728
{24,12} of size 1728
{24,12} of size 1728
{24,18} of size 1728
{24,18} of size 1728
{24,18} of size 1728
{24,6} of size 1728
{24,6} of size 1728
{24,6} of size 1728
{24,18} of size 1728
{24,6} of size 1728
{24,4} of size 1728
{24,4} of size 1728
{24,12} of size 1728
{24,4} of size 1728
{24,4} of size 1728
{24,12} of size 1728
{24,12} of size 1728
{24,12} of size 1728
{24,12} of size 1728
{24,12} of size 1728
{24,12} of size 1728
{24,12} of size 1728
{24,6} of size 1728
{24,6} of size 1728
{24,38} of size 1824
{24,20} of size 1920
{24,40} of size 1920
{24,40} of size 1920
{24,40} of size 1920
{24,40} of size 1920
{24,20} of size 1920
{24,20} of size 1920
{24,20} of size 1920
{24,30} of size 1920
{24,20} of size 1920
{24,20} of size 1920
{24,30} of size 1920
{24,10} of size 1920
{24,10} of size 1920
{24,6} of size 1920
{24,10} of size 1920
{24,4} of size 1920
{24,10} of size 1920
{24,4} of size 1920
{24,4} of size 1920
{24,6} of size 1920
{24,4} of size 1920
{24,10} of size 1920
{24,10} of size 1920
Vertex Figure Of :
{2,24} of size 96
{4,24} of size 192
{4,24} of size 192
{4,24} of size 192
{4,24} of size 192
{6,24} of size 288
{6,24} of size 288
{6,24} of size 288
{3,24} of size 288
{4,24} of size 384
{8,24} of size 384
{8,24} of size 384
{8,24} of size 384
{8,24} of size 384
{4,24} of size 384
{4,24} of size 384
{4,24} of size 384
{6,24} of size 384
{4,24} of size 384
{4,24} of size 384
{6,24} of size 384
{10,24} of size 480
{12,24} of size 576
{12,24} of size 576
{12,24} of size 576
{12,24} of size 576
{12,24} of size 576
{12,24} of size 576
{3,24} of size 576
{6,24} of size 576
{4,24} of size 576
{4,24} of size 576
{6,24} of size 576
{6,24} of size 576
{6,24} of size 576
{6,24} of size 576
{14,24} of size 672
{8,24} of size 768
{8,24} of size 768
{4,24} of size 768
{8,24} of size 768
{8,24} of size 768
{16,24} of size 768
{16,24} of size 768
{16,24} of size 768
{16,24} of size 768
{16,24} of size 768
{16,24} of size 768
{4,24} of size 768
{8,24} of size 768
{4,24} of size 768
{4,24} of size 768
{8,24} of size 768
{8,24} of size 768
{8,24} of size 768
{4,24} of size 768
{4,24} of size 768
{3,24} of size 768
{4,24} of size 768
{4,24} of size 768
{8,24} of size 768
{8,24} of size 768
{8,24} of size 768
{8,24} of size 768
{6,24} of size 768
{8,24} of size 768
{8,24} of size 768
{12,24} of size 768
{8,24} of size 768
{8,24} of size 768
{12,24} of size 768
{4,24} of size 768
{4,24} of size 768
{12,24} of size 768
{4,24} of size 768
{12,24} of size 768
{12,24} of size 768
{4,24} of size 768
{12,24} of size 768
{18,24} of size 864
{6,24} of size 864
{6,24} of size 864
{18,24} of size 864
{6,24} of size 864
{9,24} of size 864
{3,24} of size 864
{6,24} of size 864
{6,24} of size 864
{6,24} of size 864
{6,24} of size 864
{6,24} of size 864
{20,24} of size 960
{20,24} of size 960
{6,24} of size 960
{6,24} of size 960
{10,24} of size 960
{10,24} of size 960
{4,24} of size 960
{4,24} of size 960
{6,24} of size 960
{6,24} of size 960
{10,24} of size 960
{10,24} of size 960
{22,24} of size 1056
{12,24} of size 1152
{12,24} of size 1152
{12,24} of size 1152
{4,24} of size 1152
{24,24} of size 1152
{24,24} of size 1152
{24,24} of size 1152
{24,24} of size 1152
{24,24} of size 1152
{24,24} of size 1152
{24,24} of size 1152
{24,24} of size 1152
{24,24} of size 1152
{8,24} of size 1152
{8,24} of size 1152
{8,24} of size 1152
{24,24} of size 1152
{24,24} of size 1152
{24,24} of size 1152
{8,24} of size 1152
{12,24} of size 1152
{12,24} of size 1152
{12,24} of size 1152
{4,24} of size 1152
{3,24} of size 1152
{6,24} of size 1152
{12,24} of size 1152
{12,24} of size 1152
{6,24} of size 1152
{6,24} of size 1152
{12,24} of size 1152
{12,24} of size 1152
{12,24} of size 1152
{12,24} of size 1152
{12,24} of size 1152
{6,24} of size 1152
{12,24} of size 1152
{6,24} of size 1152
{6,24} of size 1152
{12,24} of size 1152
{12,24} of size 1152
{12,24} of size 1152
{12,24} of size 1152
{6,24} of size 1152
{6,24} of size 1152
{6,24} of size 1152
{12,24} of size 1152
{12,24} of size 1152
{6,24} of size 1152
{6,24} of size 1152
{6,24} of size 1152
{12,24} of size 1152
{12,24} of size 1152
{12,24} of size 1152
{6,24} of size 1152
{12,24} of size 1152
{3,24} of size 1152
{12,24} of size 1152
{12,24} of size 1152
{3,24} of size 1152
{26,24} of size 1248
{28,24} of size 1344
{28,24} of size 1344
{30,24} of size 1440
{30,24} of size 1440
{30,24} of size 1440
{6,24} of size 1440
{6,24} of size 1440
{15,24} of size 1440
{34,24} of size 1632
{36,24} of size 1728
{12,24} of size 1728
{36,24} of size 1728
{12,24} of size 1728
{36,24} of size 1728
{12,24} of size 1728
{12,24} of size 1728
{36,24} of size 1728
{12,24} of size 1728
{12,24} of size 1728
{9,24} of size 1728
{18,24} of size 1728
{3,24} of size 1728
{6,24} of size 1728
{12,24} of size 1728
{12,24} of size 1728
{4,24} of size 1728
{4,24} of size 1728
{12,24} of size 1728
{12,24} of size 1728
{4,24} of size 1728
{4,24} of size 1728
{12,24} of size 1728
{12,24} of size 1728
{12,24} of size 1728
{12,24} of size 1728
{12,24} of size 1728
{12,24} of size 1728
{18,24} of size 1728
{18,24} of size 1728
{18,24} of size 1728
{6,24} of size 1728
{6,24} of size 1728
{6,24} of size 1728
{18,24} of size 1728
{6,24} of size 1728
{4,24} of size 1728
{4,24} of size 1728
{12,24} of size 1728
{4,24} of size 1728
{4,24} of size 1728
{12,24} of size 1728
{12,24} of size 1728
{12,24} of size 1728
{12,24} of size 1728
{12,24} of size 1728
{12,24} of size 1728
{12,24} of size 1728
{6,24} of size 1728
{6,24} of size 1728
{38,24} of size 1824
{20,24} of size 1920
{40,24} of size 1920
{40,24} of size 1920
{40,24} of size 1920
{40,24} of size 1920
{20,24} of size 1920
{20,24} of size 1920
{20,24} of size 1920
{30,24} of size 1920
{20,24} of size 1920
{20,24} of size 1920
{30,24} of size 1920
{10,24} of size 1920
{10,24} of size 1920
{6,24} of size 1920
{10,24} of size 1920
{4,24} of size 1920
{10,24} of size 1920
{4,24} of size 1920
{4,24} of size 1920
{6,24} of size 1920
{4,24} of size 1920
{10,24} of size 1920
{10,24} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {12}*24
3-fold quotients : {8}*16
4-fold quotients : {6}*12
6-fold quotients : {4}*8
8-fold quotients : {3}*6
12-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
2-fold covers : {48}*96
3-fold covers : {72}*144
4-fold covers : {96}*192
5-fold covers : {120}*240
6-fold covers : {144}*288
7-fold covers : {168}*336
8-fold covers : {192}*384
9-fold covers : {216}*432
10-fold covers : {240}*480
11-fold covers : {264}*528
12-fold covers : {288}*576
13-fold covers : {312}*624
14-fold covers : {336}*672
15-fold covers : {360}*720
16-fold covers : {384}*768
17-fold covers : {408}*816
18-fold covers : {432}*864
19-fold covers : {456}*912
20-fold covers : {480}*960
21-fold covers : {504}*1008
22-fold covers : {528}*1056
23-fold covers : {552}*1104
24-fold covers : {576}*1152
25-fold covers : {600}*1200
26-fold covers : {624}*1248
27-fold covers : {648}*1296
28-fold covers : {672}*1344
29-fold covers : {696}*1392
30-fold covers : {720}*1440
31-fold covers : {744}*1488
33-fold covers : {792}*1584
34-fold covers : {816}*1632
35-fold covers : {840}*1680
36-fold covers : {864}*1728
37-fold covers : {888}*1776
38-fold covers : {912}*1824
39-fold covers : {936}*1872
40-fold covers : {960}*1920
41-fold covers : {984}*1968
Permutation Representation (GAP) :
s0 := ( 2, 3)( 4, 5)( 6, 9)( 7,11)( 8,10)(12,15)(13,17)(14,16)(19,22)(20,21)
(23,24);;
s1 := ( 1, 7)( 2, 4)( 3,13)( 5, 8)( 6,10)( 9,19)(11,14)(12,16)(15,23)(17,20)
(18,21)(22,24);;
poly := Group([s0,s1]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1");;
s0 := F.1;; s1 := F.2;;
rels := [ s0*s0, s1*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(24)!( 2, 3)( 4, 5)( 6, 9)( 7,11)( 8,10)(12,15)(13,17)(14,16)(19,22)
(20,21)(23,24);
s1 := Sym(24)!( 1, 7)( 2, 4)( 3,13)( 5, 8)( 6,10)( 9,19)(11,14)(12,16)(15,23)
(17,20)(18,21)(22,24);
poly := sub<Sym(24)|s0,s1>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1> := Group< s0,s1 | s0*s0, s1*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope