Polytope of Type {2,10,12}

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

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

Permutation Representation (Magma) :

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

to this polytope