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Polytope of Type {4,15}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,15}*240
if this polytope has a name.
Group : SmallGroup(240,197)
Rank : 3
Schlafli Type : {4,15}
Number of vertices, edges, etc : 8, 60, 30
Order of s0s1s2 : 30
Order of s0s1s2s1 : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {4,15,2} of size 480
   {4,15,4} of size 960
   {4,15,6} of size 1440
   {4,15,6} of size 1920
   {4,15,4} of size 1920
Vertex Figure Of :
   {2,4,15} of size 480
   {4,4,15} of size 960
   {6,4,15} of size 1440
   {4,4,15} of size 1920
   {8,4,15} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,15}*120
   4-fold quotients : {2,15}*60
   5-fold quotients : {4,3}*48
   10-fold quotients : {4,3}*24
   12-fold quotients : {2,5}*20
   20-fold quotients : {2,3}*12
Covers (Minimal Covers in Boldface) :
   2-fold covers : {8,15}*480, {4,30}*480
   3-fold covers : {4,45}*720, {12,15}*720
   4-fold covers : {8,15}*960a, {4,60}*960b, {4,30}*960b, {4,60}*960c, {8,30}*960b, {8,30}*960c
   5-fold covers : {4,75}*1200, {20,15}*1200
   6-fold covers : {8,45}*1440, {4,90}*1440, {24,15}*1440, {12,30}*1440a, {12,30}*1440b
   7-fold covers : {4,105}*1680
   8-fold covers : {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
Permutation Representation (GAP) :
s0 := (  1, 62)(  2, 61)(  3, 64)(  4, 63)(  5, 66)(  6, 65)(  7, 68)(  8, 67)
(  9, 70)( 10, 69)( 11, 72)( 12, 71)( 13, 74)( 14, 73)( 15, 76)( 16, 75)
( 17, 78)( 18, 77)( 19, 80)( 20, 79)( 21, 82)( 22, 81)( 23, 84)( 24, 83)
( 25, 86)( 26, 85)( 27, 88)( 28, 87)( 29, 90)( 30, 89)( 31, 92)( 32, 91)
( 33, 94)( 34, 93)( 35, 96)( 36, 95)( 37, 98)( 38, 97)( 39,100)( 40, 99)
( 41,102)( 42,101)( 43,104)( 44,103)( 45,106)( 46,105)( 47,108)( 48,107)
( 49,110)( 50,109)( 51,112)( 52,111)( 53,114)( 54,113)( 55,116)( 56,115)
( 57,118)( 58,117)( 59,120)( 60,119);;
s1 := (  2,  3)(  5, 17)(  6, 19)(  7, 18)(  8, 20)(  9, 13)( 10, 15)( 11, 14)
( 12, 16)( 21, 41)( 22, 43)( 23, 42)( 24, 44)( 25, 57)( 26, 59)( 27, 58)
( 28, 60)( 29, 53)( 30, 55)( 31, 54)( 32, 56)( 33, 49)( 34, 51)( 35, 50)
( 36, 52)( 37, 45)( 38, 47)( 39, 46)( 40, 48)( 62, 63)( 65, 77)( 66, 79)
( 67, 78)( 68, 80)( 69, 73)( 70, 75)( 71, 74)( 72, 76)( 81,101)( 82,103)
( 83,102)( 84,104)( 85,117)( 86,119)( 87,118)( 88,120)( 89,113)( 90,115)
( 91,114)( 92,116)( 93,109)( 94,111)( 95,110)( 96,112)( 97,105)( 98,107)
( 99,106)(100,108);;
s2 := (  1, 25)(  2, 26)(  3, 28)(  4, 27)(  5, 21)(  6, 22)(  7, 24)(  8, 23)
(  9, 37)( 10, 38)( 11, 40)( 12, 39)( 13, 33)( 14, 34)( 15, 36)( 16, 35)
( 17, 29)( 18, 30)( 19, 32)( 20, 31)( 41, 45)( 42, 46)( 43, 48)( 44, 47)
( 49, 57)( 50, 58)( 51, 60)( 52, 59)( 55, 56)( 61, 85)( 62, 86)( 63, 88)
( 64, 87)( 65, 81)( 66, 82)( 67, 84)( 68, 83)( 69, 97)( 70, 98)( 71,100)
( 72, 99)( 73, 93)( 74, 94)( 75, 96)( 76, 95)( 77, 89)( 78, 90)( 79, 92)
( 80, 91)(101,105)(102,106)(103,108)(104,107)(109,117)(110,118)(111,120)
(112,119)(115,116);;
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, s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1, 
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(120)!(  1, 62)(  2, 61)(  3, 64)(  4, 63)(  5, 66)(  6, 65)(  7, 68)
(  8, 67)(  9, 70)( 10, 69)( 11, 72)( 12, 71)( 13, 74)( 14, 73)( 15, 76)
( 16, 75)( 17, 78)( 18, 77)( 19, 80)( 20, 79)( 21, 82)( 22, 81)( 23, 84)
( 24, 83)( 25, 86)( 26, 85)( 27, 88)( 28, 87)( 29, 90)( 30, 89)( 31, 92)
( 32, 91)( 33, 94)( 34, 93)( 35, 96)( 36, 95)( 37, 98)( 38, 97)( 39,100)
( 40, 99)( 41,102)( 42,101)( 43,104)( 44,103)( 45,106)( 46,105)( 47,108)
( 48,107)( 49,110)( 50,109)( 51,112)( 52,111)( 53,114)( 54,113)( 55,116)
( 56,115)( 57,118)( 58,117)( 59,120)( 60,119);
s1 := Sym(120)!(  2,  3)(  5, 17)(  6, 19)(  7, 18)(  8, 20)(  9, 13)( 10, 15)
( 11, 14)( 12, 16)( 21, 41)( 22, 43)( 23, 42)( 24, 44)( 25, 57)( 26, 59)
( 27, 58)( 28, 60)( 29, 53)( 30, 55)( 31, 54)( 32, 56)( 33, 49)( 34, 51)
( 35, 50)( 36, 52)( 37, 45)( 38, 47)( 39, 46)( 40, 48)( 62, 63)( 65, 77)
( 66, 79)( 67, 78)( 68, 80)( 69, 73)( 70, 75)( 71, 74)( 72, 76)( 81,101)
( 82,103)( 83,102)( 84,104)( 85,117)( 86,119)( 87,118)( 88,120)( 89,113)
( 90,115)( 91,114)( 92,116)( 93,109)( 94,111)( 95,110)( 96,112)( 97,105)
( 98,107)( 99,106)(100,108);
s2 := Sym(120)!(  1, 25)(  2, 26)(  3, 28)(  4, 27)(  5, 21)(  6, 22)(  7, 24)
(  8, 23)(  9, 37)( 10, 38)( 11, 40)( 12, 39)( 13, 33)( 14, 34)( 15, 36)
( 16, 35)( 17, 29)( 18, 30)( 19, 32)( 20, 31)( 41, 45)( 42, 46)( 43, 48)
( 44, 47)( 49, 57)( 50, 58)( 51, 60)( 52, 59)( 55, 56)( 61, 85)( 62, 86)
( 63, 88)( 64, 87)( 65, 81)( 66, 82)( 67, 84)( 68, 83)( 69, 97)( 70, 98)
( 71,100)( 72, 99)( 73, 93)( 74, 94)( 75, 96)( 76, 95)( 77, 89)( 78, 90)
( 79, 92)( 80, 91)(101,105)(102,106)(103,108)(104,107)(109,117)(110,118)
(111,120)(112,119)(115,116);
poly := sub<Sym(120)|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, s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1, 
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 >; 
 
References : None.
to this polytope