Polytope of Type {3,2,5}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,5}*60
if this polytope has a name.
Group : SmallGroup(60,8)
Rank : 4
Schlafli Type : {3,2,5}
Number of vertices, edges, etc : 3, 3, 5, 5
Order of s₀s₁s₂s₃ : 15
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Projective
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {3,2,5,2} of size 120
   {3,2,5,3} of size 360
   {3,2,5,5} of size 360
   {3,2,5,10} of size 600
   {3,2,5,4} of size 720
   {3,2,5,6} of size 720
   {3,2,5,3} of size 720
   {3,2,5,5} of size 720
   {3,2,5,6} of size 720
   {3,2,5,6} of size 720
   {3,2,5,10} of size 720
   {3,2,5,10} of size 720
   {3,2,5,4} of size 960
   {3,2,5,5} of size 960
   {3,2,5,4} of size 1440
   {3,2,5,6} of size 1440
   {3,2,5,6} of size 1440
   {3,2,5,10} of size 1440
   {3,2,5,5} of size 1920
   {3,2,5,8} of size 1920
   {3,2,5,8} of size 1920
   {3,2,5,10} of size 1920
   {3,2,5,4} of size 1920
   {3,2,5,10} of size 1920
Vertex Figure Of :
   {2,3,2,5} of size 120
   {3,3,2,5} of size 240
   {4,3,2,5} of size 240
   {6,3,2,5} of size 360
   {4,3,2,5} of size 480
   {6,3,2,5} of size 480
   {5,3,2,5} of size 600
   {8,3,2,5} of size 960
   {12,3,2,5} of size 960
   {6,3,2,5} of size 1080
   {5,3,2,5} of size 1200
   {10,3,2,5} of size 1200
   {10,3,2,5} of size 1200
   {6,3,2,5} of size 1440
   {12,3,2,5} of size 1440
   {6,3,2,5} of size 1920
   {8,3,2,5} of size 1920
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {3,2,10}*120, {6,2,5}*120
   3-fold covers : {9,2,5}*180, {3,2,15}*180
   4-fold covers : {12,2,5}*240, {3,2,20}*240, {6,2,10}*240
   5-fold covers : {3,2,25}*300, {15,2,5}*300
   6-fold covers : {9,2,10}*360, {18,2,5}*360, {3,6,10}*360, {3,2,30}*360, {6,2,15}*360
   7-fold covers : {21,2,5}*420, {3,2,35}*420
   8-fold covers : {24,2,5}*480, {3,2,40}*480, {12,2,10}*480, {6,2,20}*480, {6,4,10}*480, {3,4,10}*480
   9-fold covers : {27,2,5}*540, {3,2,45}*540, {9,2,15}*540, {3,6,15}*540
   10-fold covers : {3,2,50}*600, {6,2,25}*600, {6,10,5}*600, {15,2,10}*600, {30,2,5}*600
   11-fold covers : {33,2,5}*660, {3,2,55}*660
   12-fold covers : {36,2,5}*720, {9,2,20}*720, {18,2,10}*720, {3,6,20}*720, {12,2,15}*720, {3,2,60}*720, {6,6,10}*720a, {6,6,10}*720c, {6,2,30}*720
   13-fold covers : {39,2,5}*780, {3,2,65}*780
   14-fold covers : {21,2,10}*840, {42,2,5}*840, {3,2,70}*840, {6,2,35}*840
   15-fold covers : {9,2,25}*900, {3,2,75}*900, {45,2,5}*900, {15,2,15}*900
   16-fold covers : {48,2,5}*960, {3,2,80}*960, {12,2,20}*960, {12,4,10}*960, {6,4,20}*960, {24,2,10}*960, {6,2,40}*960, {6,8,10}*960, {3,4,20}*960, {3,8,10}*960, {6,4,10}*960
   17-fold covers : {51,2,5}*1020, {3,2,85}*1020
   18-fold covers : {27,2,10}*1080, {54,2,5}*1080, {9,6,10}*1080, {3,6,10}*1080, {3,2,90}*1080, {6,2,45}*1080, {9,2,30}*1080, {18,2,15}*1080, {3,6,30}*1080a, {6,6,15}*1080a, {3,6,30}*1080b, {6,6,15}*1080b
   19-fold covers : {57,2,5}*1140, {3,2,95}*1140
   20-fold covers : {12,2,25}*1200, {3,2,100}*1200, {6,2,50}*1200, {12,10,5}*1200, {15,2,20}*1200, {60,2,5}*1200, {6,10,10}*1200a, {6,10,10}*1200b, {30,2,10}*1200
   21-fold covers : {63,2,5}*1260, {9,2,35}*1260, {21,2,15}*1260, {3,2,105}*1260
   22-fold covers : {33,2,10}*1320, {66,2,5}*1320, {3,2,110}*1320, {6,2,55}*1320
   23-fold covers : {69,2,5}*1380, {3,2,115}*1380
   24-fold covers : {72,2,5}*1440, {9,2,40}*1440, {36,2,10}*1440, {18,2,20}*1440, {18,4,10}*1440, {3,6,40}*1440, {24,2,15}*1440, {3,2,120}*1440, {9,4,10}*1440, {6,12,10}*1440a, {12,6,10}*1440a, {12,6,10}*1440b, {6,6,20}*1440a, {6,6,20}*1440c, {6,12,10}*1440c, {12,2,30}*1440, {6,2,60}*1440, {6,4,30}*1440, {3,6,10}*1440, {3,12,10}*1440, {6,6,15}*1440, {6,4,15}*1440, {3,4,30}*1440
   25-fold covers : {3,2,125}*1500, {75,2,5}*1500, {15,2,25}*1500, {15,10,5}*1500, {3,10,5}*1500
   26-fold covers : {39,2,10}*1560, {78,2,5}*1560, {3,2,130}*1560, {6,2,65}*1560
   27-fold covers : {81,2,5}*1620, {9,2,45}*1620, {3,6,45}*1620, {9,6,15}*1620, {3,2,135}*1620, {27,2,15}*1620, {3,6,15}*1620a, {3,6,15}*1620b
   28-fold covers : {21,2,20}*1680, {84,2,5}*1680, {12,2,35}*1680, {3,2,140}*1680, {6,14,10}*1680, {42,2,10}*1680, {6,2,70}*1680
   29-fold covers : {87,2,5}*1740, {3,2,145}*1740
   30-fold covers : {9,2,50}*1800, {18,2,25}*1800, {3,6,50}*1800, {3,2,150}*1800, {6,2,75}*1800, {18,10,5}*1800, {45,2,10}*1800, {90,2,5}*1800, {6,10,15}*1800, {15,6,10}*1800, {15,2,30}*1800, {30,2,15}*1800
   31-fold covers : {93,2,5}*1860, {3,2,155}*1860
   32-fold covers : {96,2,5}*1920, {3,2,160}*1920, {12,4,20}*1920, {12,8,10}*1920a, {6,8,20}*1920a, {24,4,10}*1920a, {6,4,40}*1920a, {12,8,10}*1920b, {6,8,20}*1920b, {24,4,10}*1920b, {6,4,40}*1920b, {12,4,10}*1920a, {6,4,20}*1920a, {12,2,40}*1920, {24,2,20}*1920, {6,16,10}*1920, {48,2,10}*1920, {6,2,80}*1920, {3,8,20}*1920, {3,4,20}*1920, {3,8,10}*1920, {3,4,40}*1920, {12,4,10}*1920b, {6,4,20}*1920b, {6,4,10}*1920, {12,4,10}*1920c, {6,8,10}*1920a, {6,8,10}*1920b, {6,4,5}*1920
   33-fold covers : {99,2,5}*1980, {9,2,55}*1980, {33,2,15}*1980, {3,2,165}*1980
Permutation Representation (GAP) :

s0 := (2,3);;
s1 := (1,2);;
s2 := (5,6)(7,8);;
s3 := (4,5)(6,7);;
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, 
s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(8)!(2,3);
s1 := Sym(8)!(1,2);
s2 := Sym(8)!(5,6)(7,8);
s3 := Sym(8)!(4,5)(6,7);
poly := sub<Sym(8)|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, s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

to this polytope