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Polytope of Type {8,2,24}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,2,24}*768
if this polytope has a name.
Group : SmallGroup(768,161916)
Rank : 4
Schlafli Type : {8,2,24}
Number of vertices, edges, etc : 8, 8, 24, 24
Order of s0s1s2s3 : 24
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,2,24}*384, {8,2,12}*384
   3-fold quotients : {8,2,8}*256
   4-fold quotients : {4,2,12}*192, {2,2,24}*192, {8,2,6}*192
   6-fold quotients : {4,2,8}*128, {8,2,4}*128
   8-fold quotients : {8,2,3}*96, {2,2,12}*96, {4,2,6}*96
   12-fold quotients : {4,2,4}*64, {2,2,8}*64, {8,2,2}*64
   16-fold quotients : {4,2,3}*48, {2,2,6}*48
   24-fold quotients : {2,2,4}*32, {4,2,2}*32
   32-fold quotients : {2,2,3}*24
   48-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (2,3)(4,5)(6,7);;
s1 := (1,2)(3,4)(5,6)(7,8);;
s2 := (10,11)(12,13)(14,17)(15,19)(16,18)(20,23)(21,25)(22,24)(27,30)(28,29)
(31,32);;
s3 := ( 9,15)(10,12)(11,21)(13,16)(14,18)(17,27)(19,22)(20,24)(23,31)(25,28)
(26,29)(30,32);;
poly := Group([s0,s1,s2,s3]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(32)!(2,3)(4,5)(6,7);
s1 := Sym(32)!(1,2)(3,4)(5,6)(7,8);
s2 := Sym(32)!(10,11)(12,13)(14,17)(15,19)(16,18)(20,23)(21,25)(22,24)(27,30)
(28,29)(31,32);
s3 := Sym(32)!( 9,15)(10,12)(11,21)(13,16)(14,18)(17,27)(19,22)(20,24)(23,31)
(25,28)(26,29)(30,32);
poly := sub<Sym(32)|s0,s1,s2,s3>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >; 
 

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