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Polytope of Type {5,3}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {5,3}*60
Also Known As : hemidodecahedron, {5,3}5if this polytope has another name.
Group : SmallGroup(60,5)
Rank : 3
Schlafli Type : {5,3}
Number of vertices, edges, etc : 10, 15, 6
Order of s0s1s2 : 5
Order of s0s1s2s1 : 5
Special Properties :
   Projective
   Locally Spherical
   Non-Orientable
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {5,3,2} of size 120
   {5,3,4} of size 1920
Vertex Figure Of :
   {2,5,3} of size 120
   {3,5,3} of size 660
   {4,5,3} of size 960
   {6,5,3} of size 1320
   {4,5,3} of size 1920
   {4,5,3} of size 1920
   {4,5,3} of size 1920
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {5,3}*120, {5,6}*120b, {5,6}*120c, {10,3}*120a, {10,3}*120b
   4-fold covers : {5,6}*240b, {10,3}*240, {10,6}*240c, {10,6}*240d, {10,6}*240e, {10,6}*240f
   6-fold covers : {10,3}*360, {15,3}*360, {15,6}*360
   8-fold covers : {10,12}*480c, {10,12}*480d, {20,6}*480a, {20,6}*480b, {5,12}*480, {20,3}*480, {10,6}*480c
   10-fold covers : {5,6}*600, {5,15}*600, {10,15}*600
   12-fold covers : {10,3}*720b, {10,6}*720b, {10,6}*720c, {15,6}*720c, {15,6}*720d, {30,3}*720, {30,6}*720a, {30,6}*720b
   14-fold covers : {10,21}*840, {35,6}*840
   16-fold covers : {10,24}*960c, {10,24}*960d, {40,6}*960a, {40,6}*960b, {10,12}*960c, {20,6}*960c, {10,12}*960d, {20,6}*960d, {10,6}*960b, {5,6}*960
   18-fold covers : {10,9}*1080, {45,6}*1080
   20-fold covers : {5,6}*1200b, {5,30}*1200b, {10,6}*1200a, {10,6}*1200b, {10,15}*1200a, {10,15}*1200b, {10,30}*1200b, {10,30}*1200c
   22-fold covers : {10,33}*1320, {55,6}*1320
   24-fold covers : {10,12}*1440e, {10,12}*1440f, {60,6}*1440a, {60,6}*1440b, {15,12}*1440a, {15,12}*1440b, {20,3}*1440a, {60,3}*1440, {15,3}*1440, {15,12}*1440d, {20,3}*1440b, {10,6}*1440f, {30,6}*1440e, {30,6}*1440f
   26-fold covers : {10,39}*1560, {65,6}*1560
   28-fold covers : {10,21}*1680, {10,42}*1680b, {10,42}*1680c, {35,6}*1680c, {70,6}*1680a, {70,6}*1680b
   30-fold covers : {10,15}*1800b, {15,6}*1800, {15,15}*1800b
   32-fold covers : {10,48}*1920c, {10,48}*1920d, {80,6}*1920a, {80,6}*1920b, {20,12}*1920g, {10,24}*1920d, {40,6}*1920f, {10,12}*1920c, {20,6}*1920d, {20,12}*1920k, {20,12}*1920l, {20,12}*1920m, {10,24}*1920f, {40,6}*1920h, {10,6}*1920a, {5,6}*1920b, {5,6}*1920c, {5,6}*1920d, {10,6}*1920b, {10,6}*1920c, {10,6}*1920d, {10,6}*1920e, {5,12}*1920c, {5,12}*1920d, {5,12}*1920e, {5,12}*1920f
Permutation Representation (GAP) :
s0 := (2,3)(4,5);;
s1 := (1,2)(3,4);;
s2 := (2,5)(3,4);;
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*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(5)!(2,3)(4,5);
s1 := Sym(5)!(1,2)(3,4);
s2 := Sym(5)!(2,5)(3,4);
poly := sub<Sym(5)|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*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1 >; 
 
References : None.
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