Polytope of Type {2,12,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,12,10}*1200
if this polytope has a name.
Group : SmallGroup(1200,1002)
Rank : 4
Schlafli Type : {2,12,10}
Number of vertices, edges, etc : 2, 30, 150, 25
Order of s₀s₁s₂s₃ : 12
Order of s₀s₁s₂s₃s₂s₁ : 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) :
   3-fold quotients : {2,4,10}*400
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope