# Polytope of Type {6,12}

Atlas Canonical Name : {6,12}*960a
if this polytope has a name.
Group : SmallGroup(960,10877)
Rank : 3
Schlafli Type : {6,12}
Number of vertices, edges, etc : 40, 240, 80
Order of s0s1s2 : 6
Order of s0s1s2s1 : 20
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Self-Petrie
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
{6,12,2} of size 1920
Vertex Figure Of :
{2,6,12} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {6,6}*480
4-fold quotients : {6,6}*240a, {6,6}*240b, {6,6}*240c
8-fold quotients : {6,6}*120
120-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
2-fold covers : {6,12}*1920a, {12,12}*1920b, {12,12}*1920c
Permutation Representation (GAP) :
s0 := ( 2,26)( 3,75)( 4,80)( 5,41)( 6,70)( 7,68)( 8,43)( 9,19)(10,13)(11,12)
(15,64)(17,44)(18,47)(21,33)(22,39)(23,42)(24,78)(27,36)(28,79)(29,55)(30,53)
(31,52)(32,54)(35,37)(38,76)(40,77)(45,48)(46,63)(49,62)(50,72)(51,59)(56,57)
(60,67)(65,71)(66,69)(73,74);;
s1 := ( 2,22)( 3,21)( 4,37)( 5,80)( 6,48)( 7,44)( 8,13)( 9,11)(10,63)(12,69)
(14,68)(15,64)(16,62)(17,61)(18,70)(19,47)(20,34)(23,40)(24,52)(26,32)(27,33)
(28,76)(29,79)(30,42)(31,74)(36,39)(45,66)(49,71)(50,59)(51,57)(53,78)(54,75)
(58,65)(73,77);;
s2 := ( 1,14)( 2,64)( 3,66)( 4,65)( 5,12)( 6,74)( 7,52)( 8,35)( 9,55)(10,54)
(11,41)(13,32)(15,26)(16,25)(17,28)(18,27)(19,29)(20,61)(21,60)(22,59)(23,62)
(24,63)(30,57)(31,68)(33,67)(34,58)(36,47)(37,43)(38,50)(39,51)(40,48)(42,49)
(44,79)(45,77)(46,78)(53,56)(69,75)(70,73)(71,80)(72,76);;
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, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1 ];;
poly := F / rels;;

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

References : None.
to this polytope