Polytope of Type {5,2,3}

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

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

Permutation Representation (Magma) :

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

to this polytope