Polytope of Type {2,15}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,15}*60
if this polytope has a name.
Group : SmallGroup(60,12)
Rank : 3
Schlafli Type : {2,15}
Number of vertices, edges, etc : 2, 15, 15
Order of s₀s₁s₂ : 30
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,15,2} of size 120
   {2,15,4} of size 240
   {2,15,6} of size 360
   {2,15,6} of size 480
   {2,15,4} of size 480
   {2,15,10} of size 600
   {2,15,3} of size 720
   {2,15,6} of size 720
   {2,15,10} of size 720
   {2,15,12} of size 960
   {2,15,8} of size 960
   {2,15,4} of size 960
   {2,15,6} of size 1080
   {2,15,5} of size 1200
   {2,15,10} of size 1200
   {2,15,4} of size 1440
   {2,15,6} of size 1440
   {2,15,6} of size 1440
   {2,15,6} of size 1440
   {2,15,6} of size 1440
   {2,15,10} of size 1440
   {2,15,12} of size 1440
   {2,15,6} of size 1440
   {2,15,30} of size 1800
   {2,15,6} of size 1920
   {2,15,8} of size 1920
   {2,15,8} of size 1920
   {2,15,8} of size 1920
   {2,15,10} of size 1920
   {2,15,4} of size 1920
Vertex Figure Of :
   {2,2,15} of size 120
   {3,2,15} of size 180
   {4,2,15} of size 240
   {5,2,15} of size 300
   {6,2,15} of size 360
   {7,2,15} of size 420
   {8,2,15} of size 480
   {9,2,15} of size 540
   {10,2,15} of size 600
   {11,2,15} of size 660
   {12,2,15} of size 720
   {13,2,15} of size 780
   {14,2,15} of size 840
   {15,2,15} of size 900
   {16,2,15} of size 960
   {17,2,15} of size 1020
   {18,2,15} of size 1080
   {19,2,15} of size 1140
   {20,2,15} of size 1200
   {21,2,15} of size 1260
   {22,2,15} of size 1320
   {23,2,15} of size 1380
   {24,2,15} of size 1440
   {25,2,15} of size 1500
   {26,2,15} of size 1560
   {27,2,15} of size 1620
   {28,2,15} of size 1680
   {29,2,15} of size 1740
   {30,2,15} of size 1800
   {31,2,15} of size 1860
   {32,2,15} of size 1920
   {33,2,15} of size 1980
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {2,5}*20
   5-fold quotients : {2,3}*12
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,30}*120
   3-fold covers : {2,45}*180, {6,15}*180
   4-fold covers : {2,60}*240, {4,30}*240a, {4,15}*240
   5-fold covers : {2,75}*300, {10,15}*300
   6-fold covers : {2,90}*360, {6,30}*360b, {6,30}*360c
   7-fold covers : {2,105}*420
   8-fold covers : {4,60}*480a, {2,120}*480, {8,30}*480, {8,15}*480, {4,30}*480
   9-fold covers : {2,135}*540, {6,45}*540, {6,15}*540
   10-fold covers : {2,150}*600, {10,30}*600b, {10,30}*600c
   11-fold covers : {2,165}*660
   12-fold covers : {2,180}*720, {4,90}*720a, {4,45}*720, {12,30}*720b, {6,60}*720b, {6,60}*720c, {12,30}*720c, {12,15}*720, {6,15}*720e
   13-fold covers : {2,195}*780
   14-fold covers : {14,30}*840, {2,210}*840
   15-fold covers : {2,225}*900, {6,75}*900, {10,45}*900, {30,15}*900
   16-fold covers : {4,120}*960a, {4,60}*960a, {4,120}*960b, {8,60}*960a, {8,60}*960b, {2,240}*960, {16,30}*960, {8,15}*960a, {4,60}*960b, {4,30}*960b, {4,60}*960c, {8,30}*960b, {8,30}*960c, {4,15}*960
   17-fold covers : {2,255}*1020
   18-fold covers : {2,270}*1080, {6,90}*1080a, {6,90}*1080b, {18,30}*1080b, {6,30}*1080b, {6,30}*1080c, {6,30}*1080d
   19-fold covers : {2,285}*1140
   20-fold covers : {2,300}*1200, {4,150}*1200a, {4,75}*1200, {20,30}*1200b, {10,60}*1200b, {10,60}*1200c, {20,30}*1200c, {20,15}*1200
   21-fold covers : {2,315}*1260, {6,105}*1260
   22-fold covers : {22,30}*1320, {2,330}*1320
   23-fold covers : {2,345}*1380
   24-fold covers : {4,180}*1440a, {2,360}*1440, {8,90}*1440, {8,45}*1440, {24,30}*1440b, {6,120}*1440b, {6,120}*1440c, {12,60}*1440b, {12,60}*1440c, {24,30}*1440c, {4,90}*1440, {24,15}*1440, {12,15}*1440c, {12,30}*1440a, {12,30}*1440b, {6,30}*1440h, {6,60}*1440d
   25-fold covers : {2,375}*1500, {10,75}*1500, {10,15}*1500e, {10,15}*1500g
   26-fold covers : {26,30}*1560, {2,390}*1560
   27-fold covers : {2,405}*1620, {18,45}*1620, {6,45}*1620a, {6,135}*1620, {6,45}*1620b, {6,45}*1620c, {6,45}*1620d, {6,15}*1620, {18,15}*1620
   28-fold covers : {14,60}*1680, {28,30}*1680a, {2,420}*1680, {4,210}*1680a, {4,105}*1680
   29-fold covers : {2,435}*1740
   30-fold covers : {2,450}*1800, {6,150}*1800b, {6,150}*1800c, {10,90}*1800b, {10,90}*1800c, {30,30}*1800c, {30,30}*1800d, {30,30}*1800g, {30,30}*1800h
   31-fold covers : {2,465}*1860
   32-fold covers : {8,60}*1920a, {4,120}*1920a, {8,120}*1920a, {8,120}*1920b, {8,120}*1920c, {8,120}*1920d, {16,60}*1920a, {4,240}*1920a, {16,60}*1920b, {4,240}*1920b, {4,60}*1920a, {4,120}*1920b, {8,60}*1920b, {32,30}*1920, {2,480}*1920, {8,15}*1920a, {8,30}*1920a, {4,60}*1920d, {8,60}*1920e, {8,60}*1920f, {4,30}*1920a, {8,30}*1920d, {8,30}*1920e, {8,30}*1920f, {8,60}*1920g, {8,60}*1920h, {4,120}*1920c, {4,120}*1920d, {8,30}*1920g, {4,60}*1920e, {4,120}*1920e, {4,30}*1920b, {4,120}*1920f, {8,15}*1920b, {4,15}*1920a, {4,30}*1920c, {8,15}*1920c, {4,30}*1920d
   33-fold covers : {2,495}*1980, {6,165}*1980
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := ( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13)(14,15)(16,17);;
s2 := ( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16);;
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*s1*s0*s1, s0*s2*s0*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(17)!(1,2);
s1 := Sym(17)!( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13)(14,15)(16,17);
s2 := Sym(17)!( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16);
poly := sub<Sym(17)|s0,s1,s2>;

Finitely Presented Group Representation (Magma) :

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

to this polytope