Polytope of Type {30,10,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {30,10,2}*1200a
if this polytope has a name.
Group : SmallGroup(1200,1006)
Rank : 4
Schlafli Type : {30,10,2}
Number of vertices, edges, etc : 30, 150, 10, 2
Order of s₀s₁s₂s₃ : 30
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   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) :
   3-fold quotients : {10,10,2}*400b
   5-fold quotients : {6,10,2}*240
   6-fold quotients : {10,5,2}*200
   15-fold quotients : {2,10,2}*80
   25-fold quotients : {6,2,2}*48
   30-fold quotients : {2,5,2}*40
   50-fold quotients : {3,2,2}*24
   75-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

to this polytope