Polytope of Type {45,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {45,2}*180
if this polytope has a name.
Group : SmallGroup(180,11)
Rank : 3
Schlafli Type : {45,2}
Number of vertices, edges, etc : 45, 45, 2
Order of s₀s₁s₂ : 90
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {45,2,2} of size 360
   {45,2,3} of size 540
   {45,2,4} of size 720
   {45,2,5} of size 900
   {45,2,6} of size 1080
   {45,2,7} of size 1260
   {45,2,8} of size 1440
   {45,2,9} of size 1620
   {45,2,10} of size 1800
   {45,2,11} of size 1980
Vertex Figure Of :
   {2,45,2} of size 360
   {4,45,2} of size 720
   {6,45,2} of size 1080
   {4,45,2} of size 1440
   {10,45,2} of size 1800
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {15,2}*60
   5-fold quotients : {9,2}*36
   9-fold quotients : {5,2}*20
   15-fold quotients : {3,2}*12
Covers (Minimal Covers in Boldface) :
   2-fold covers : {90,2}*360
   3-fold covers : {135,2}*540, {45,6}*540
   4-fold covers : {180,2}*720, {90,4}*720a, {45,4}*720
   5-fold covers : {225,2}*900, {45,10}*900
   6-fold covers : {270,2}*1080, {90,6}*1080a, {90,6}*1080b
   7-fold covers : {315,2}*1260
   8-fold covers : {180,4}*1440a, {360,2}*1440, {90,8}*1440, {45,8}*1440, {90,4}*1440
   9-fold covers : {405,2}*1620, {45,18}*1620, {45,6}*1620a, {135,6}*1620
   10-fold covers : {450,2}*1800, {90,10}*1800b, {90,10}*1800c
   11-fold covers : {495,2}*1980
Permutation Representation (GAP) :

s0 := ( 2, 3)( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)
(22,23)(24,25)(26,27)(28,29)(30,31)(32,33)(34,35)(36,37)(38,39)(40,41)(42,43)
(44,45);;
s1 := ( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)
(21,22)(23,24)(25,26)(27,28)(29,30)(31,32)(33,34)(35,36)(37,38)(39,40)(41,42)
(43,44);;
s2 := (46,47);;
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 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(47)!( 2, 3)( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13)(14,15)(16,17)(18,19)
(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)(32,33)(34,35)(36,37)(38,39)(40,41)
(42,43)(44,45);
s1 := Sym(47)!( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)
(19,20)(21,22)(23,24)(25,26)(27,28)(29,30)(31,32)(33,34)(35,36)(37,38)(39,40)
(41,42)(43,44);
s2 := Sym(47)!(46,47);
poly := sub<Sym(47)|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 >;

to this polytope