Polytope of Type {30,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {30,6}*480
if this polytope has a name.
Group : SmallGroup(480,1193)
Rank : 3
Schlafli Type : {30,6}
Number of vertices, edges, etc : 40, 120, 8
Order of s₀s₁s₂ : 20
Order of s₀s₁s₂s₁ : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {30,6,2} of size 960
   {30,6,4} of size 1920
Vertex Figure Of :
   {2,30,6} of size 960
   {4,30,6} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {15,6}*240
   5-fold quotients : {6,6}*96
   10-fold quotients : {3,6}*48, {6,3}*48
   12-fold quotients : {10,2}*40
   20-fold quotients : {3,3}*24
   24-fold quotients : {5,2}*20
   60-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {60,6}*960a, {30,12}*960a, {30,6}*960, {60,6}*960b, {30,12}*960b
   3-fold covers : {30,6}*1440g, {30,6}*1440h
   4-fold covers : {30,6}*1920a, {60,12}*1920a, {60,12}*1920b, {60,6}*1920, {30,6}*1920b, {30,6}*1920c, {120,6}*1920a, {120,6}*1920b, {60,12}*1920c, {30,24}*1920a, {30,12}*1920, {60,12}*1920d, {30,24}*1920b
Permutation Representation (GAP) :

s0 := (  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);;
s1 := (  1, 85)(  2, 86)(  3, 88)(  4, 87)(  5, 81)(  6, 82)(  7, 84)(  8, 83)
(  9, 97)( 10, 98)( 11,100)( 12, 99)( 13, 93)( 14, 94)( 15, 96)( 16, 95)
( 17, 89)( 18, 90)( 19, 92)( 20, 91)( 21, 65)( 22, 66)( 23, 68)( 24, 67)
( 25, 61)( 26, 62)( 27, 64)( 28, 63)( 29, 77)( 30, 78)( 31, 80)( 32, 79)
( 33, 73)( 34, 74)( 35, 76)( 36, 75)( 37, 69)( 38, 70)( 39, 72)( 40, 71)
( 41,105)( 42,106)( 43,108)( 44,107)( 45,101)( 46,102)( 47,104)( 48,103)
( 49,117)( 50,118)( 51,120)( 52,119)( 53,113)( 54,114)( 55,116)( 56,115)
( 57,109)( 58,110)( 59,112)( 60,111);;
s2 := (  1,  4)(  5,  8)(  9, 12)( 13, 16)( 17, 20)( 21, 44)( 22, 42)( 23, 43)
( 24, 41)( 25, 48)( 26, 46)( 27, 47)( 28, 45)( 29, 52)( 30, 50)( 31, 51)
( 32, 49)( 33, 56)( 34, 54)( 35, 55)( 36, 53)( 37, 60)( 38, 58)( 39, 59)
( 40, 57)( 61, 64)( 65, 68)( 69, 72)( 73, 76)( 77, 80)( 81,104)( 82,102)
( 83,103)( 84,101)( 85,108)( 86,106)( 87,107)( 88,105)( 89,112)( 90,110)
( 91,111)( 92,109)( 93,116)( 94,114)( 95,115)( 96,113)( 97,120)( 98,118)
( 99,119)(100,117);;
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*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, 
s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := 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);
s1 := Sym(120)!(  1, 85)(  2, 86)(  3, 88)(  4, 87)(  5, 81)(  6, 82)(  7, 84)
(  8, 83)(  9, 97)( 10, 98)( 11,100)( 12, 99)( 13, 93)( 14, 94)( 15, 96)
( 16, 95)( 17, 89)( 18, 90)( 19, 92)( 20, 91)( 21, 65)( 22, 66)( 23, 68)
( 24, 67)( 25, 61)( 26, 62)( 27, 64)( 28, 63)( 29, 77)( 30, 78)( 31, 80)
( 32, 79)( 33, 73)( 34, 74)( 35, 76)( 36, 75)( 37, 69)( 38, 70)( 39, 72)
( 40, 71)( 41,105)( 42,106)( 43,108)( 44,107)( 45,101)( 46,102)( 47,104)
( 48,103)( 49,117)( 50,118)( 51,120)( 52,119)( 53,113)( 54,114)( 55,116)
( 56,115)( 57,109)( 58,110)( 59,112)( 60,111);
s2 := Sym(120)!(  1,  4)(  5,  8)(  9, 12)( 13, 16)( 17, 20)( 21, 44)( 22, 42)
( 23, 43)( 24, 41)( 25, 48)( 26, 46)( 27, 47)( 28, 45)( 29, 52)( 30, 50)
( 31, 51)( 32, 49)( 33, 56)( 34, 54)( 35, 55)( 36, 53)( 37, 60)( 38, 58)
( 39, 59)( 40, 57)( 61, 64)( 65, 68)( 69, 72)( 73, 76)( 77, 80)( 81,104)
( 82,102)( 83,103)( 84,101)( 85,108)( 86,106)( 87,107)( 88,105)( 89,112)
( 90,110)( 91,111)( 92,109)( 93,116)( 94,114)( 95,115)( 96,113)( 97,120)
( 98,118)( 99,119)(100,117);
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*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, 
s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s2 >;

References : None.
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