Polytope of Type {2,24}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,24}*96
if this polytope has a name.
Group : SmallGroup(96,110)
Rank : 3
Schlafli Type : {2,24}
Number of vertices, edges, etc : 2, 24, 24
Order of s₀s₁s₂ : 24
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,24,2} of size 192
   {2,24,4} of size 384
   {2,24,4} of size 384
   {2,24,4} of size 384
   {2,24,4} of size 384
   {2,24,6} of size 576
   {2,24,6} of size 576
   {2,24,6} of size 576
   {2,24,3} of size 576
   {2,24,4} of size 768
   {2,24,8} of size 768
   {2,24,8} of size 768
   {2,24,8} of size 768
   {2,24,8} of size 768
   {2,24,4} of size 768
   {2,24,4} of size 768
   {2,24,4} of size 768
   {2,24,6} of size 768
   {2,24,4} of size 768
   {2,24,6} of size 768
   {2,24,4} of size 768
   {2,24,10} of size 960
   {2,24,12} of size 1152
   {2,24,12} of size 1152
   {2,24,12} of size 1152
   {2,24,4} of size 1152
   {2,24,12} of size 1152
   {2,24,12} of size 1152
   {2,24,12} of size 1152
   {2,24,4} of size 1152
   {2,24,3} of size 1152
   {2,24,6} of size 1152
   {2,24,6} of size 1152
   {2,24,6} of size 1152
   {2,24,6} of size 1152
   {2,24,6} of size 1152
   {2,24,14} of size 1344
   {2,24,18} of size 1728
   {2,24,6} of size 1728
   {2,24,6} of size 1728
   {2,24,18} of size 1728
   {2,24,6} of size 1728
   {2,24,9} of size 1728
   {2,24,3} of size 1728
   {2,24,6} of size 1728
   {2,24,6} of size 1728
   {2,24,6} of size 1728
   {2,24,6} of size 1728
   {2,24,6} of size 1728
   {2,24,20} of size 1920
   {2,24,20} of size 1920
   {2,24,6} of size 1920
   {2,24,6} of size 1920
   {2,24,10} of size 1920
   {2,24,10} of size 1920
   {2,24,10} of size 1920
   {2,24,10} of size 1920
   {2,24,4} of size 1920
   {2,24,4} of size 1920
   {2,24,6} of size 1920
   {2,24,6} of size 1920
Vertex Figure Of :
   {2,2,24} of size 192
   {3,2,24} of size 288
   {4,2,24} of size 384
   {5,2,24} of size 480
   {6,2,24} of size 576
   {7,2,24} of size 672
   {8,2,24} of size 768
   {9,2,24} of size 864
   {10,2,24} of size 960
   {11,2,24} of size 1056
   {12,2,24} of size 1152
   {13,2,24} of size 1248
   {14,2,24} of size 1344
   {15,2,24} of size 1440
   {17,2,24} of size 1632
   {18,2,24} of size 1728
   {19,2,24} of size 1824
   {20,2,24} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,12}*48
   3-fold quotients : {2,8}*32
   4-fold quotients : {2,6}*24
   6-fold quotients : {2,4}*16
   8-fold quotients : {2,3}*12
   12-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,24}*192a, {2,48}*192
   3-fold covers : {2,72}*288, {6,24}*288a, {6,24}*288b
   4-fold covers : {4,24}*384a, {8,24}*384a, {8,24}*384b, {4,48}*384a, {4,48}*384b, {2,96}*384, {4,24}*384c
   5-fold covers : {10,24}*480, {2,120}*480
   6-fold covers : {4,72}*576a, {2,144}*576, {6,48}*576a, {6,48}*576b, {12,24}*576c, {12,24}*576d
   7-fold covers : {14,24}*672, {2,168}*672
   8-fold covers : {8,24}*768a, {4,24}*768a, {8,24}*768d, {4,48}*768a, {4,48}*768b, {16,24}*768a, {16,24}*768b, {8,48}*768c, {8,48}*768d, {16,24}*768d, {8,48}*768e, {8,48}*768f, {16,24}*768f, {4,96}*768a, {4,96}*768b, {2,192}*768, {8,24}*768i, {8,24}*768k, {4,24}*768i, {4,48}*768c, {4,48}*768d
   9-fold covers : {2,216}*864, {6,72}*864a, {6,72}*864b, {18,24}*864a, {6,24}*864a, {6,24}*864b, {6,24}*864f, {6,24}*864h
   10-fold covers : {10,48}*960, {20,24}*960a, {4,120}*960a, {2,240}*960
   11-fold covers : {22,24}*1056, {2,264}*1056
   12-fold covers : {4,72}*1152a, {12,24}*1152a, {12,24}*1152b, {8,72}*1152b, {8,72}*1152c, {24,24}*1152a, {24,24}*1152b, {24,24}*1152h, {24,24}*1152i, {4,144}*1152a, {12,48}*1152a, {12,48}*1152b, {4,144}*1152b, {12,48}*1152d, {12,48}*1152e, {2,288}*1152, {6,96}*1152b, {6,96}*1152c, {4,72}*1152c, {12,24}*1152o, {12,24}*1152p, {6,24}*1152g, {6,24}*1152h
   13-fold covers : {26,24}*1248, {2,312}*1248
   14-fold covers : {14,48}*1344, {28,24}*1344a, {4,168}*1344a, {2,336}*1344
   15-fold covers : {10,72}*1440, {2,360}*1440, {30,24}*1440a, {30,24}*1440b, {6,120}*1440b, {6,120}*1440c
   17-fold covers : {34,24}*1632, {2,408}*1632
   18-fold covers : {4,216}*1728a, {2,432}*1728, {6,144}*1728a, {6,144}*1728b, {18,48}*1728a, {6,48}*1728a, {6,48}*1728b, {12,72}*1728a, {12,72}*1728b, {36,24}*1728c, {12,24}*1728c, {12,24}*1728d, {6,48}*1728f, {12,24}*1728o, {4,24}*1728e, {4,24}*1728f, {6,48}*1728h, {12,24}*1728u
   19-fold covers : {38,24}*1824, {2,456}*1824
   20-fold covers : {4,120}*1920a, {20,24}*1920a, {8,120}*1920b, {8,120}*1920c, {40,24}*1920a, {40,24}*1920b, {4,240}*1920a, {20,48}*1920a, {4,240}*1920b, {20,48}*1920b, {2,480}*1920, {10,96}*1920, {20,24}*1920c, {4,120}*1920c
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := ( 4, 5)( 6, 7)( 8,11)( 9,13)(10,12)(14,17)(15,19)(16,18)(21,24)(22,23)
(25,26);;
s2 := ( 3, 9)( 4, 6)( 5,15)( 7,10)( 8,12)(11,21)(13,16)(14,18)(17,25)(19,22)
(20,23)(24,26);;
poly := Group([s0,s1,s2]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s1*s0*s1, s0*s2*s0*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(26)!(1,2);
s1 := Sym(26)!( 4, 5)( 6, 7)( 8,11)( 9,13)(10,12)(14,17)(15,19)(16,18)(21,24)
(22,23)(25,26);
s2 := Sym(26)!( 3, 9)( 4, 6)( 5,15)( 7,10)( 8,12)(11,21)(13,16)(14,18)(17,25)
(19,22)(20,23)(24,26);
poly := sub<Sym(26)|s0,s1,s2>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s1*s0*s1, s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

to this polytope