Polytope of Type {72,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {72,2}*288
if this polytope has a name.
Group : SmallGroup(288,114)
Rank : 3
Schlafli Type : {72,2}
Number of vertices, edges, etc : 72, 72, 2
Order of s₀s₁s₂ : 72
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {72,2,2} of size 576
   {72,2,3} of size 864
   {72,2,4} of size 1152
   {72,2,5} of size 1440
   {72,2,6} of size 1728
Vertex Figure Of :
   {2,72,2} of size 576
   {4,72,2} of size 1152
   {4,72,2} of size 1152
   {4,72,2} of size 1152
   {4,72,2} of size 1152
   {6,72,2} of size 1728
   {6,72,2} of size 1728
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {36,2}*144
   3-fold quotients : {24,2}*96
   4-fold quotients : {18,2}*72
   6-fold quotients : {12,2}*48
   8-fold quotients : {9,2}*36
   9-fold quotients : {8,2}*32
   12-fold quotients : {6,2}*24
   18-fold quotients : {4,2}*16
   24-fold quotients : {3,2}*12
   36-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {72,4}*576a, {144,2}*576
   3-fold covers : {216,2}*864, {72,6}*864a, {72,6}*864b
   4-fold covers : {72,4}*1152a, {72,8}*1152b, {72,8}*1152c, {144,4}*1152a, {144,4}*1152b, {288,2}*1152, {72,4}*1152c
   5-fold covers : {72,10}*1440, {360,2}*1440
   6-fold covers : {216,4}*1728a, {432,2}*1728, {144,6}*1728a, {144,6}*1728b, {72,12}*1728a, {72,12}*1728b
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope