Polytope of Type {30,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {30,6}*360c
if this polytope has a name.
Group : SmallGroup(360,154)
Rank : 3
Schlafli Type : {30,6}
Number of vertices, edges, etc : 30, 90, 6
Order of s₀s₁s₂ : 30
Order of s₀s₁s₂s₁ : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {30,6,2} of size 720
   {30,6,3} of size 1080
   {30,6,4} of size 1440
Vertex Figure Of :
   {2,30,6} of size 720
   {4,30,6} of size 1440
   {4,30,6} of size 1440
   {4,30,6} of size 1440
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {15,6}*180
   3-fold quotients : {30,2}*120
   5-fold quotients : {6,6}*72c
   6-fold quotients : {15,2}*60
   9-fold quotients : {10,2}*40
   10-fold quotients : {3,6}*36
   15-fold quotients : {6,2}*24
   18-fold quotients : {5,2}*20
   30-fold quotients : {3,2}*12
   45-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {60,6}*720c, {30,12}*720c
   3-fold covers : {90,6}*1080b, {30,6}*1080b, {30,6}*1080d
   4-fold covers : {120,6}*1440c, {60,12}*1440c, {30,24}*1440c, {30,12}*1440b, {30,6}*1440h
   5-fold covers : {150,6}*1800c, {30,30}*1800a, {30,30}*1800i
Permutation Representation (GAP) :

s0 := ( 2, 5)( 3, 4)( 6,11)( 7,15)( 8,14)( 9,13)(10,12)(16,31)(17,35)(18,34)
(19,33)(20,32)(21,41)(22,45)(23,44)(24,43)(25,42)(26,36)(27,40)(28,39)(29,38)
(30,37)(47,50)(48,49)(51,56)(52,60)(53,59)(54,58)(55,57)(61,76)(62,80)(63,79)
(64,78)(65,77)(66,86)(67,90)(68,89)(69,88)(70,87)(71,81)(72,85)(73,84)(74,83)
(75,82);;
s1 := ( 1,67)( 2,66)( 3,70)( 4,69)( 5,68)( 6,62)( 7,61)( 8,65)( 9,64)(10,63)
(11,72)(12,71)(13,75)(14,74)(15,73)(16,52)(17,51)(18,55)(19,54)(20,53)(21,47)
(22,46)(23,50)(24,49)(25,48)(26,57)(27,56)(28,60)(29,59)(30,58)(31,82)(32,81)
(33,85)(34,84)(35,83)(36,77)(37,76)(38,80)(39,79)(40,78)(41,87)(42,86)(43,90)
(44,89)(45,88);;
s2 := (16,31)(17,32)(18,33)(19,34)(20,35)(21,36)(22,37)(23,38)(24,39)(25,40)
(26,41)(27,42)(28,43)(29,44)(30,45)(61,76)(62,77)(63,78)(64,79)(65,80)(66,81)
(67,82)(68,83)(69,84)(70,85)(71,86)(72,87)(73,88)(74,89)(75,90);;
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*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*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(90)!( 2, 5)( 3, 4)( 6,11)( 7,15)( 8,14)( 9,13)(10,12)(16,31)(17,35)
(18,34)(19,33)(20,32)(21,41)(22,45)(23,44)(24,43)(25,42)(26,36)(27,40)(28,39)
(29,38)(30,37)(47,50)(48,49)(51,56)(52,60)(53,59)(54,58)(55,57)(61,76)(62,80)
(63,79)(64,78)(65,77)(66,86)(67,90)(68,89)(69,88)(70,87)(71,81)(72,85)(73,84)
(74,83)(75,82);
s1 := Sym(90)!( 1,67)( 2,66)( 3,70)( 4,69)( 5,68)( 6,62)( 7,61)( 8,65)( 9,64)
(10,63)(11,72)(12,71)(13,75)(14,74)(15,73)(16,52)(17,51)(18,55)(19,54)(20,53)
(21,47)(22,46)(23,50)(24,49)(25,48)(26,57)(27,56)(28,60)(29,59)(30,58)(31,82)
(32,81)(33,85)(34,84)(35,83)(36,77)(37,76)(38,80)(39,79)(40,78)(41,87)(42,86)
(43,90)(44,89)(45,88);
s2 := Sym(90)!(16,31)(17,32)(18,33)(19,34)(20,35)(21,36)(22,37)(23,38)(24,39)
(25,40)(26,41)(27,42)(28,43)(29,44)(30,45)(61,76)(62,77)(63,78)(64,79)(65,80)
(66,81)(67,82)(68,83)(69,84)(70,85)(71,86)(72,87)(73,88)(74,89)(75,90);
poly := sub<Sym(90)|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*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*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