Polytope of Type {2,15,4,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,15,4,4}*1920a
if this polytope has a name.
Group : SmallGroup(1920,239472)
Rank : 5
Schlafli Type : {2,15,4,4}
Number of vertices, edges, etc : 2, 15, 60, 16, 8
Order of s₀s₁s₂s₃s₄ : 30
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Non-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 : {2,15,4,2}*480
   5-fold quotients : {2,3,4,4}*384a
   20-fold quotients : {2,3,4,2}*96
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := ( 5, 6)( 7,11)( 8,12)( 9,14)(10,13)(17,18)(19,67)(20,68)(21,70)(22,69)
(23,75)(24,76)(25,78)(26,77)(27,71)(28,72)(29,74)(30,73)(31,79)(32,80)(33,82)
(34,81)(35,51)(36,52)(37,54)(38,53)(39,59)(40,60)(41,62)(42,61)(43,55)(44,56)
(45,58)(46,57)(47,63)(48,64)(49,66)(50,65);;
s2 := ( 3,19)( 4,22)( 5,21)( 6,20)( 7,23)( 8,26)( 9,25)(10,24)(11,31)(12,34)
(13,33)(14,32)(15,27)(16,30)(17,29)(18,28)(35,67)(36,70)(37,69)(38,68)(39,71)
(40,74)(41,73)(42,72)(43,79)(44,82)(45,81)(46,80)(47,75)(48,78)(49,77)(50,76)
(52,54)(56,58)(59,63)(60,66)(61,65)(62,64);;
s3 := ( 3,15)( 4,16)( 5,17)( 6,18)( 7,11)( 8,12)( 9,13)(10,14)(19,31)(20,32)
(21,33)(22,34)(23,27)(24,28)(25,29)(26,30)(35,47)(36,48)(37,49)(38,50)(39,43)
(40,44)(41,45)(42,46)(51,63)(52,64)(53,65)(54,66)(55,59)(56,60)(57,61)(58,62)
(67,79)(68,80)(69,81)(70,82)(71,75)(72,76)(73,77)(74,78);;
s4 := ( 7, 9)( 8,10)(11,14)(12,13)(15,16)(17,18)(23,25)(24,26)(27,30)(28,29)
(31,32)(33,34)(39,41)(40,42)(43,46)(44,45)(47,48)(49,50)(55,57)(56,58)(59,62)
(60,61)(63,64)(65,66)(71,73)(72,74)(75,78)(76,77)(79,80)(81,82);;
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*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s2*s3*s2*s3*s2*s3*s2*s3, s3*s4*s3*s4*s3*s4*s3*s4, 
s3*s2*s1*s3*s2*s3*s2*s1*s2, s4*s2*s3*s4*s2*s3*s4*s2*s3*s4*s2*s3, 
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(82)!(1,2);
s1 := Sym(82)!( 5, 6)( 7,11)( 8,12)( 9,14)(10,13)(17,18)(19,67)(20,68)(21,70)
(22,69)(23,75)(24,76)(25,78)(26,77)(27,71)(28,72)(29,74)(30,73)(31,79)(32,80)
(33,82)(34,81)(35,51)(36,52)(37,54)(38,53)(39,59)(40,60)(41,62)(42,61)(43,55)
(44,56)(45,58)(46,57)(47,63)(48,64)(49,66)(50,65);
s2 := Sym(82)!( 3,19)( 4,22)( 5,21)( 6,20)( 7,23)( 8,26)( 9,25)(10,24)(11,31)
(12,34)(13,33)(14,32)(15,27)(16,30)(17,29)(18,28)(35,67)(36,70)(37,69)(38,68)
(39,71)(40,74)(41,73)(42,72)(43,79)(44,82)(45,81)(46,80)(47,75)(48,78)(49,77)
(50,76)(52,54)(56,58)(59,63)(60,66)(61,65)(62,64);
s3 := Sym(82)!( 3,15)( 4,16)( 5,17)( 6,18)( 7,11)( 8,12)( 9,13)(10,14)(19,31)
(20,32)(21,33)(22,34)(23,27)(24,28)(25,29)(26,30)(35,47)(36,48)(37,49)(38,50)
(39,43)(40,44)(41,45)(42,46)(51,63)(52,64)(53,65)(54,66)(55,59)(56,60)(57,61)
(58,62)(67,79)(68,80)(69,81)(70,82)(71,75)(72,76)(73,77)(74,78);
s4 := Sym(82)!( 7, 9)( 8,10)(11,14)(12,13)(15,16)(17,18)(23,25)(24,26)(27,30)
(28,29)(31,32)(33,34)(39,41)(40,42)(43,46)(44,45)(47,48)(49,50)(55,57)(56,58)
(59,62)(60,61)(63,64)(65,66)(71,73)(72,74)(75,78)(76,77)(79,80)(81,82);
poly := sub<Sym(82)|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*s1*s0*s1, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4, s3*s2*s1*s3*s2*s3*s2*s1*s2, 
s4*s2*s3*s4*s2*s3*s4*s2*s3*s4*s2*s3, 
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