Polytope of Type {15,8,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {15,8,2}*1920a
if this polytope has a name.
Group : SmallGroup(1920,239473)
Rank : 4
Schlafli Type : {15,8,2}
Number of vertices, edges, etc : 60, 240, 32, 2
Order of s₀s₁s₂s₃ : 30
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) :
   4-fold quotients : {15,4,2}*480
   5-fold quotients : {3,8,2}*384
   8-fold quotients : {15,4,2}*240
   16-fold quotients : {15,2,2}*120
   20-fold quotients : {3,4,2}*96
   40-fold quotients : {3,4,2}*48
   48-fold quotients : {5,2,2}*40
   80-fold quotients : {3,2,2}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := ( 3, 4)( 5,10)( 6, 9)( 7,11)( 8,12)(15,16)(17,65)(18,66)(19,68)(20,67)
(21,74)(22,73)(23,75)(24,76)(25,70)(26,69)(27,71)(28,72)(29,77)(30,78)(31,80)
(32,79)(33,49)(34,50)(35,52)(36,51)(37,58)(38,57)(39,59)(40,60)(41,54)(42,53)
(43,55)(44,56)(45,61)(46,62)(47,64)(48,63);;
s1 := ( 1,17)( 2,19)( 3,18)( 4,20)( 5,21)( 6,23)( 7,22)( 8,24)( 9,31)(10,29)
(11,32)(12,30)(13,26)(14,28)(15,25)(16,27)(33,65)(34,67)(35,66)(36,68)(37,69)
(38,71)(39,70)(40,72)(41,79)(42,77)(43,80)(44,78)(45,74)(46,76)(47,73)(48,75)
(50,51)(54,55)(57,63)(58,61)(59,64)(60,62);;
s2 := ( 1,13)( 2,14)( 3,15)( 4,16)( 5, 9)( 6,10)( 7,11)( 8,12)(17,29)(18,30)
(19,31)(20,32)(21,25)(22,26)(23,27)(24,28)(33,45)(34,46)(35,47)(36,48)(37,41)
(38,42)(39,43)(40,44)(49,61)(50,62)(51,63)(52,64)(53,57)(54,58)(55,59)(56,60)
(65,77)(66,78)(67,79)(68,80)(69,73)(70,74)(71,75)(72,76);;
s3 := (81,82);;
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, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s2*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(82)!( 3, 4)( 5,10)( 6, 9)( 7,11)( 8,12)(15,16)(17,65)(18,66)(19,68)
(20,67)(21,74)(22,73)(23,75)(24,76)(25,70)(26,69)(27,71)(28,72)(29,77)(30,78)
(31,80)(32,79)(33,49)(34,50)(35,52)(36,51)(37,58)(38,57)(39,59)(40,60)(41,54)
(42,53)(43,55)(44,56)(45,61)(46,62)(47,64)(48,63);
s1 := Sym(82)!( 1,17)( 2,19)( 3,18)( 4,20)( 5,21)( 6,23)( 7,22)( 8,24)( 9,31)
(10,29)(11,32)(12,30)(13,26)(14,28)(15,25)(16,27)(33,65)(34,67)(35,66)(36,68)
(37,69)(38,71)(39,70)(40,72)(41,79)(42,77)(43,80)(44,78)(45,74)(46,76)(47,73)
(48,75)(50,51)(54,55)(57,63)(58,61)(59,64)(60,62);
s2 := Sym(82)!( 1,13)( 2,14)( 3,15)( 4,16)( 5, 9)( 6,10)( 7,11)( 8,12)(17,29)
(18,30)(19,31)(20,32)(21,25)(22,26)(23,27)(24,28)(33,45)(34,46)(35,47)(36,48)
(37,41)(38,42)(39,43)(40,44)(49,61)(50,62)(51,63)(52,64)(53,57)(54,58)(55,59)
(56,60)(65,77)(66,78)(67,79)(68,80)(69,73)(70,74)(71,75)(72,76);
s3 := Sym(82)!(81,82);
poly := sub<Sym(82)|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, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s2*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 >;

to this polytope