Polytope of Type {2,5,10,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,5,10,6}*1200
if this polytope has a name.
Group : SmallGroup(1200,1006)
Rank : 5
Schlafli Type : {2,5,10,6}
Number of vertices, edges, etc : 2, 5, 25, 30, 6
Order of s₀s₁s₂s₃s₄ : 30
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 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 : {2,5,10,2}*400
   5-fold quotients : {2,5,2,6}*240
   10-fold quotients : {2,5,2,3}*120
   15-fold quotients : {2,5,2,2}*80
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, 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);;
s3 := ( 4, 7)( 5, 6)( 9,12)(10,11)(14,17)(15,16)(19,22)(20,21)(24,27)(25,26)
(28,53)(29,57)(30,56)(31,55)(32,54)(33,58)(34,62)(35,61)(36,60)(37,59)(38,63)
(39,67)(40,66)(41,65)(42,64)(43,68)(44,72)(45,71)(46,70)(47,69)(48,73)(49,77)
(50,76)(51,75)(52,74);;
s4 := ( 3,28)( 4,29)( 5,30)( 6,31)( 7,32)( 8,33)( 9,34)(10,35)(11,36)(12,37)
(13,38)(14,39)(15,40)(16,41)(17,42)(18,43)(19,44)(20,45)(21,46)(22,47)(23,48)
(24,49)(25,50)(26,51)(27,52);;
poly := Group([s0,s1,s2,s3,s4]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s2*s3*s4*s3*s2*s3*s4*s3, s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
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, 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);
s3 := Sym(77)!( 4, 7)( 5, 6)( 9,12)(10,11)(14,17)(15,16)(19,22)(20,21)(24,27)
(25,26)(28,53)(29,57)(30,56)(31,55)(32,54)(33,58)(34,62)(35,61)(36,60)(37,59)
(38,63)(39,67)(40,66)(41,65)(42,64)(43,68)(44,72)(45,71)(46,70)(47,69)(48,73)
(49,77)(50,76)(51,75)(52,74);
s4 := Sym(77)!( 3,28)( 4,29)( 5,30)( 6,31)( 7,32)( 8,33)( 9,34)(10,35)(11,36)
(12,37)(13,38)(14,39)(15,40)(16,41)(17,42)(18,43)(19,44)(20,45)(21,46)(22,47)
(23,48)(24,49)(25,50)(26,51)(27,52);
poly := sub<Sym(77)|s0,s1,s2,s3,s4>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s2*s3*s4*s3*s2*s3*s4*s3, 
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;

to this polytope