Polytope of Type {15,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {15,10}*300
if this polytope has a name.
Group : SmallGroup(300,39)
Rank : 3
Schlafli Type : {15,10}
Number of vertices, edges, etc : 15, 75, 10
Order of s₀s₁s₂ : 30
Order of s₀s₁s₂s₁ : 10
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {15,10,2} of size 600
   {15,10,4} of size 1200
   {15,10,5} of size 1500
   {15,10,6} of size 1800
Vertex Figure Of :
   {2,15,10} of size 600
   {4,15,10} of size 1200
   {6,15,10} of size 1800
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {5,10}*100
   5-fold quotients : {15,2}*60
   15-fold quotients : {5,2}*20
   25-fold quotients : {3,2}*12
Covers (Minimal Covers in Boldface) :
   2-fold covers : {30,10}*600c
   3-fold covers : {45,10}*900, {15,30}*900
   4-fold covers : {60,10}*1200c, {30,20}*1200c, {15,20}*1200
   5-fold covers : {75,10}*1500, {15,10}*1500e
   6-fold covers : {90,10}*1800c, {30,30}*1800f, {30,30}*1800i
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope