Polytope of Type {44,6}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {44,6}*792
if this polytope has a name.
Group : SmallGroup(792,113)
Rank : 3
Schlafli Type : {44,6}
Number of vertices, edges, etc : 66, 198, 9
Order of s₀s₁s₂ : 44
Order of s₀s₁s₂s₁ : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {44,6,2} of size 1584
Vertex Figure Of :
   {2,44,6} of size 1584
Quotients (Maximal Quotients in Boldface) :
   11-fold quotients : {4,6}*72
Covers (Minimal Covers in Boldface) :
   2-fold covers : {44,6}*1584
Irregular Quotients (of which this is a minimal cover):
   None.

Permutation Representation (GAP) :

s0 := ( 2,11)( 3,10)( 4, 9)( 5, 8)( 6, 7)(12,78)(13,88)(14,87)(15,86)(16,85)(17,84)(18,83)(19,82)(20,81)(21,80)(22,79)(23,56)(24,66)(25,65)(26,64)(27,63)(28,62)(29,61)(30,60)(31,59)(32,58)(33,57)(34,67)(35,77)(36,76)(37,75)(38,74)(39,73)(40,72)(41,71)(42,70)(43,69)(44,68)(46,55)(47,54)(48,53)(49,52)(50,51)(90,99)(91,98)(92,97)(93,96)(94,95);;
s1 := ( 1, 2)( 3,11)( 4,10)( 5, 9)( 6, 8)(12,24)(13,23)(14,33)(15,32)(16,31)(17,30)(18,29)(19,28)(20,27)(21,26)(22,25)(34,46)(35,45)(36,55)(37,54)(38,53)(39,52)(40,51)(41,50)(42,49)(43,48)(44,47)(56,57)(58,66)(59,65)(60,64)(61,63)(67,90)(68,89)(69,99)(70,98)(71,97)(72,96)(73,95)(74,94)(75,93)(76,92)(77,91)(78,79)(80,88)(81,87)(82,86)(83,85);;
s2 := ( 1,45)( 2,46)( 3,47)( 4,48)( 5,49)( 6,50)( 7,51)( 8,52)( 9,53)(10,54)(11,55)(12,34)(13,35)(14,36)(15,37)(16,38)(17,39)(18,40)(19,41)(20,42)(21,43)(22,44)(23,56)(24,57)(25,58)(26,59)(27,60)(28,61)(29,62)(30,63)(31,64)(32,65)(33,66)(67,78)(68,79)(69,80)(70,81)(71,82)(72,83)(73,84)(74,85)(75,86)(76,87)(77,88);;
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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s2*s1*s2*s0*s1*s2*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*s2*s1*s0*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(99)!( 2,11)( 3,10)( 4, 9)( 5, 8)( 6, 7)(12,78)(13,88)(14,87)(15,86)(16,85)(17,84)(18,83)(19,82)(20,81)(21,80)(22,79)(23,56)(24,66)(25,65)(26,64)(27,63)(28,62)(29,61)(30,60)(31,59)(32,58)(33,57)(34,67)(35,77)(36,76)(37,75)(38,74)(39,73)(40,72)(41,71)(42,70)(43,69)(44,68)(46,55)(47,54)(48,53)(49,52)(50,51)(90,99)(91,98)(92,97)(93,96)(94,95);
s1 := Sym(99)!( 1, 2)( 3,11)( 4,10)( 5, 9)( 6, 8)(12,24)(13,23)(14,33)(15,32)(16,31)(17,30)(18,29)(19,28)(20,27)(21,26)(22,25)(34,46)(35,45)(36,55)(37,54)(38,53)(39,52)(40,51)(41,50)(42,49)(43,48)(44,47)(56,57)(58,66)(59,65)(60,64)(61,63)(67,90)(68,89)(69,99)(70,98)(71,97)(72,96)(73,95)(74,94)(75,93)(76,92)(77,91)(78,79)(80,88)(81,87)(82,86)(83,85);
s2 := Sym(99)!( 1,45)( 2,46)( 3,47)( 4,48)( 5,49)( 6,50)( 7,51)( 8,52)( 9,53)(10,54)(11,55)(12,34)(13,35)(14,36)(15,37)(16,38)(17,39)(18,40)(19,41)(20,42)(21,43)(22,44)(23,56)(24,57)(25,58)(26,59)(27,60)(28,61)(29,62)(30,63)(31,64)(32,65)(33,66)(67,78)(68,79)(69,80)(70,81)(71,82)(72,83)(73,84)(74,85)(75,86)(76,87)(77,88);
poly := sub<Sym(99)|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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s2*s1*s2*s0*s1*s2*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*s2*s1*s0*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

References : None.
to this polytope

Polytope of Type {44,6}

Twisty Puzzle