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