Polytope of Type {4,15,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,15,4}*480
if this polytope has a name.
Group : SmallGroup(480,1201)
Rank : 4
Schlafli Type : {4,15,4}
Number of vertices, edges, etc : 4, 30, 30, 4
Order of s₀s₁s₂s₃ : 15
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Universal
   Non-Orientable
   Flat
   Self-Dual
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {4,15,4,2} of size 960
Vertex Figure Of :
   {2,4,15,4} of size 960
Quotients (Maximal Quotients in Boldface) :
   5-fold quotients : {4,3,4}*96
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,15,4}*960a, {4,15,4}*960b, {4,30,4}*960d, {4,30,4}*960e, {4,30,4}*960f, {4,30,4}*960g
   3-fold covers : {4,45,4}*1440
   4-fold covers : {4,60,4}*1920f, {4,60,4}*1920g, {4,60,4}*1920h, {4,60,4}*1920i, {4,15,8}*1920, {8,15,4}*1920, {4,15,4}*1920c, {4,30,4}*1920c, {4,30,4}*1920d, {4,30,4}*1920e, {4,30,4}*1920f
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope