Polytope of Type {15,2,3}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {15,2,3}*180
if this polytope has a name.
Group : SmallGroup(180,29)
Rank : 4
Schlafli Type : {15,2,3}
Number of vertices, edges, etc : 15, 15, 3, 3
Order of s₀s₁s₂s₃ : 15
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {15,2,3,2} of size 360
   {15,2,3,3} of size 720
   {15,2,3,4} of size 720
   {15,2,3,6} of size 1080
   {15,2,3,4} of size 1440
   {15,2,3,6} of size 1440
   {15,2,3,5} of size 1800
Vertex Figure Of :
   {2,15,2,3} of size 360
   {4,15,2,3} of size 720
   {6,15,2,3} of size 1080
   {6,15,2,3} of size 1440
   {4,15,2,3} of size 1440
   {10,15,2,3} of size 1800
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {5,2,3}*60
   5-fold quotients : {3,2,3}*36
Covers (Minimal Covers in Boldface) :
   2-fold covers : {15,2,6}*360, {30,2,3}*360
   3-fold covers : {45,2,3}*540, {15,2,9}*540, {15,6,3}*540
   4-fold covers : {15,2,12}*720, {60,2,3}*720, {30,2,6}*720
   5-fold covers : {75,2,3}*900, {15,2,15}*900
   6-fold covers : {45,2,6}*1080, {90,2,3}*1080, {15,2,18}*1080, {30,2,9}*1080, {15,6,6}*1080a, {30,6,3}*1080a, {15,6,6}*1080b, {30,6,3}*1080b
   7-fold covers : {15,2,21}*1260, {105,2,3}*1260
   8-fold covers : {15,2,24}*1440, {120,2,3}*1440, {30,2,12}*1440, {60,2,6}*1440, {30,4,6}*1440, {15,4,6}*1440, {30,4,3}*1440
   9-fold covers : {45,2,9}*1620, {45,6,3}*1620, {15,6,9}*1620, {135,2,3}*1620, {15,2,27}*1620, {15,6,3}*1620a, {15,6,3}*1620b
   10-fold covers : {75,2,6}*1800, {150,2,3}*1800, {15,10,6}*1800, {15,2,30}*1800, {30,2,15}*1800
   11-fold covers : {15,2,33}*1980, {165,2,3}*1980
Permutation Representation (GAP) :

s0 := ( 2, 3)( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13)(14,15);;
s1 := ( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14);;
s2 := (17,18);;
s3 := (16,17);;
poly := Group([s0,s1,s2,s3]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3*s2*s3, 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(18)!( 2, 3)( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13)(14,15);
s1 := Sym(18)!( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14);
s2 := Sym(18)!(17,18);
s3 := Sym(18)!(16,17);
poly := sub<Sym(18)|s0,s1,s2,s3>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3*s2*s3, 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