Polytope of Type {15,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {15,4}*1920b
if this polytope has a name.
Group : SmallGroup(1920,240395)
Rank : 3
Schlafli Type : {15,4}
Number of vertices, edges, etc : 240, 480, 64
Order of s₀s₁s₂ : 15
Order of s₀s₁s₂s₁ : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
   Skewing Operation
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   4-fold quotients : {15,4}*480
   12-fold quotients : {5,4}*160
   16-fold quotients : {15,4}*120
   80-fold quotients : {3,4}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Finitely Presented Group Representation (Magma) :

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