Polytope of Type {24,6,2,3}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24,6,2,3}*1728c
if this polytope has a name.
Group : SmallGroup(1728,37593)
Rank : 5
Schlafli Type : {24,6,2,3}
Number of vertices, edges, etc : 24, 72, 6, 3, 3
Order of s₀s₁s₂s₃s₄ : 24
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 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 : {12,6,2,3}*864c
   3-fold quotients : {8,6,2,3}*576
   4-fold quotients : {6,6,2,3}*432b
   6-fold quotients : {4,6,2,3}*288a
   8-fold quotients : {6,3,2,3}*216
   9-fold quotients : {8,2,2,3}*192
   12-fold quotients : {2,6,2,3}*144
   18-fold quotients : {4,2,2,3}*96
   24-fold quotients : {2,3,2,3}*72
   36-fold quotients : {2,2,2,3}*48
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := ( 4, 7)( 5, 8)( 6, 9)(13,16)(14,17)(15,18)(19,28)(20,29)(21,30)(22,34)
(23,35)(24,36)(25,31)(26,32)(27,33)(37,55)(38,56)(39,57)(40,61)(41,62)(42,63)
(43,58)(44,59)(45,60)(46,64)(47,65)(48,66)(49,70)(50,71)(51,72)(52,67)(53,68)
(54,69);;
s1 := ( 1,40)( 2,42)( 3,41)( 4,37)( 5,39)( 6,38)( 7,43)( 8,45)( 9,44)(10,49)
(11,51)(12,50)(13,46)(14,48)(15,47)(16,52)(17,54)(18,53)(19,67)(20,69)(21,68)
(22,64)(23,66)(24,65)(25,70)(26,72)(27,71)(28,58)(29,60)(30,59)(31,55)(32,57)
(33,56)(34,61)(35,63)(36,62);;
s2 := ( 1, 2)( 4, 8)( 5, 7)( 6, 9)(10,11)(13,17)(14,16)(15,18)(19,20)(22,26)
(23,25)(24,27)(28,29)(31,35)(32,34)(33,36)(37,38)(40,44)(41,43)(42,45)(46,47)
(49,53)(50,52)(51,54)(55,56)(58,62)(59,61)(60,63)(64,65)(67,71)(68,70)
(69,72);;
s3 := (74,75);;
s4 := (73,74);;
poly := Group([s0,s1,s2,s3,s4]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s3*s4*s3*s4*s3*s4, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1, 
s2*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(75)!( 4, 7)( 5, 8)( 6, 9)(13,16)(14,17)(15,18)(19,28)(20,29)(21,30)
(22,34)(23,35)(24,36)(25,31)(26,32)(27,33)(37,55)(38,56)(39,57)(40,61)(41,62)
(42,63)(43,58)(44,59)(45,60)(46,64)(47,65)(48,66)(49,70)(50,71)(51,72)(52,67)
(53,68)(54,69);
s1 := Sym(75)!( 1,40)( 2,42)( 3,41)( 4,37)( 5,39)( 6,38)( 7,43)( 8,45)( 9,44)
(10,49)(11,51)(12,50)(13,46)(14,48)(15,47)(16,52)(17,54)(18,53)(19,67)(20,69)
(21,68)(22,64)(23,66)(24,65)(25,70)(26,72)(27,71)(28,58)(29,60)(30,59)(31,55)
(32,57)(33,56)(34,61)(35,63)(36,62);
s2 := Sym(75)!( 1, 2)( 4, 8)( 5, 7)( 6, 9)(10,11)(13,17)(14,16)(15,18)(19,20)
(22,26)(23,25)(24,27)(28,29)(31,35)(32,34)(33,36)(37,38)(40,44)(41,43)(42,45)
(46,47)(49,53)(50,52)(51,54)(55,56)(58,62)(59,61)(60,63)(64,65)(67,71)(68,70)
(69,72);
s3 := Sym(75)!(74,75);
s4 := Sym(75)!(73,74);
poly := sub<Sym(75)|s0,s1,s2,s3,s4>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4*s3*s4, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1, 
s2*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1 >;

to this polytope