# Polytope of Type {36,6}

Atlas Canonical Name : {36,6}*432c
if this polytope has a name.
Group : SmallGroup(432,521)
Rank : 3
Schlafli Type : {36,6}
Number of vertices, edges, etc : 36, 108, 6
Order of s0s1s2 : 9
Order of s0s1s2s1 : 4
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Non-Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
{36,6,2} of size 864
{36,6,4} of size 1728
Vertex Figure Of :
{2,36,6} of size 864
{4,36,6} of size 1728
Quotients (Maximal Quotients in Boldface) :
3-fold quotients : {12,6}*144d
9-fold quotients : {4,6}*48b
18-fold quotients : {4,3}*24
Covers (Minimal Covers in Boldface) :
2-fold covers : {36,6}*864
3-fold covers : {108,6}*1296c, {36,18}*1296d, {36,6}*1296k
4-fold covers : {72,6}*1728a, {36,12}*1728c, {36,6}*1728b, {72,6}*1728b, {72,6}*1728c, {36,12}*1728d, {36,12}*1728i
Permutation Representation (GAP) :
s0 := ( 1, 3)( 2, 4)( 5,11)( 6,12)( 7, 9)( 8,10)(13,31)(14,32)(15,29)(16,30)
(17,27)(18,28)(19,25)(20,26)(21,35)(22,36)(23,33)(24,34);;
s1 := ( 1,13)( 2,15)( 3,14)( 4,16)( 5,21)( 6,23)( 7,22)( 8,24)( 9,17)(10,19)
(11,18)(12,20)(25,29)(26,31)(27,30)(28,32)(34,35);;
s2 := ( 2, 4)( 6, 8)(10,12)(14,16)(18,20)(22,24)(26,28)(30,32)(34,36);;
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,
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1,
s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :
s0 := Sym(36)!( 1, 3)( 2, 4)( 5,11)( 6,12)( 7, 9)( 8,10)(13,31)(14,32)(15,29)
(16,30)(17,27)(18,28)(19,25)(20,26)(21,35)(22,36)(23,33)(24,34);
s1 := Sym(36)!( 1,13)( 2,15)( 3,14)( 4,16)( 5,21)( 6,23)( 7,22)( 8,24)( 9,17)
(10,19)(11,18)(12,20)(25,29)(26,31)(27,30)(28,32)(34,35);
s2 := Sym(36)!( 2, 4)( 6, 8)(10,12)(14,16)(18,20)(22,24)(26,28)(30,32)(34,36);
poly := sub<Sym(36)|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,
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1,
s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s2 >;

References : None.
to this polytope