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Polytope of Type {30,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {30,8}*480
Also Known As : {30,8|2}. if this polytope has another name.
Group : SmallGroup(480,875)
Rank : 3
Schlafli Type : {30,8}
Number of vertices, edges, etc : 30, 120, 8
Order of s0s1s2 : 120
Order of s0s1s2s1 : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {30,8,2} of size 960
   {30,8,4} of size 1920
   {30,8,4} of size 1920
Vertex Figure Of :
   {2,30,8} of size 960
   {4,30,8} of size 1920
   {4,30,8} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {30,4}*240a
   3-fold quotients : {10,8}*160
   4-fold quotients : {30,2}*120
   5-fold quotients : {6,8}*96
   6-fold quotients : {10,4}*80
   8-fold quotients : {15,2}*60
   10-fold quotients : {6,4}*48a
   12-fold quotients : {10,2}*40
   15-fold quotients : {2,8}*32
   20-fold quotients : {6,2}*24
   24-fold quotients : {5,2}*20
   30-fold quotients : {2,4}*16
   40-fold quotients : {3,2}*12
   60-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {60,8}*960a, {30,16}*960
   3-fold covers : {90,8}*1440, {30,24}*1440b, {30,24}*1440c
   4-fold covers : {60,8}*1920a, {120,8}*1920a, {120,8}*1920c, {60,16}*1920a, {60,16}*1920b, {30,32}*1920, {30,8}*1920g
Permutation Representation (GAP) :
s0 := (  2,  5)(  3,  4)(  6, 11)(  7, 15)(  8, 14)(  9, 13)( 10, 12)( 17, 20)
( 18, 19)( 21, 26)( 22, 30)( 23, 29)( 24, 28)( 25, 27)( 32, 35)( 33, 34)
( 36, 41)( 37, 45)( 38, 44)( 39, 43)( 40, 42)( 47, 50)( 48, 49)( 51, 56)
( 52, 60)( 53, 59)( 54, 58)( 55, 57)( 62, 65)( 63, 64)( 66, 71)( 67, 75)
( 68, 74)( 69, 73)( 70, 72)( 77, 80)( 78, 79)( 81, 86)( 82, 90)( 83, 89)
( 84, 88)( 85, 87)( 92, 95)( 93, 94)( 96,101)( 97,105)( 98,104)( 99,103)
(100,102)(107,110)(108,109)(111,116)(112,120)(113,119)(114,118)(115,117);;
s1 := (  1,  7)(  2,  6)(  3, 10)(  4,  9)(  5,  8)( 11, 12)( 13, 15)( 16, 22)
( 17, 21)( 18, 25)( 19, 24)( 20, 23)( 26, 27)( 28, 30)( 31, 52)( 32, 51)
( 33, 55)( 34, 54)( 35, 53)( 36, 47)( 37, 46)( 38, 50)( 39, 49)( 40, 48)
( 41, 57)( 42, 56)( 43, 60)( 44, 59)( 45, 58)( 61, 97)( 62, 96)( 63,100)
( 64, 99)( 65, 98)( 66, 92)( 67, 91)( 68, 95)( 69, 94)( 70, 93)( 71,102)
( 72,101)( 73,105)( 74,104)( 75,103)( 76,112)( 77,111)( 78,115)( 79,114)
( 80,113)( 81,107)( 82,106)( 83,110)( 84,109)( 85,108)( 86,117)( 87,116)
( 88,120)( 89,119)( 90,118);;
s2 := (  1, 61)(  2, 62)(  3, 63)(  4, 64)(  5, 65)(  6, 66)(  7, 67)(  8, 68)
(  9, 69)( 10, 70)( 11, 71)( 12, 72)( 13, 73)( 14, 74)( 15, 75)( 16, 76)
( 17, 77)( 18, 78)( 19, 79)( 20, 80)( 21, 81)( 22, 82)( 23, 83)( 24, 84)
( 25, 85)( 26, 86)( 27, 87)( 28, 88)( 29, 89)( 30, 90)( 31,106)( 32,107)
( 33,108)( 34,109)( 35,110)( 36,111)( 37,112)( 38,113)( 39,114)( 40,115)
( 41,116)( 42,117)( 43,118)( 44,119)( 45,120)( 46, 91)( 47, 92)( 48, 93)
( 49, 94)( 50, 95)( 51, 96)( 52, 97)( 53, 98)( 54, 99)( 55,100)( 56,101)
( 57,102)( 58,103)( 59,104)( 60,105);;
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*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(120)!(  2,  5)(  3,  4)(  6, 11)(  7, 15)(  8, 14)(  9, 13)( 10, 12)
( 17, 20)( 18, 19)( 21, 26)( 22, 30)( 23, 29)( 24, 28)( 25, 27)( 32, 35)
( 33, 34)( 36, 41)( 37, 45)( 38, 44)( 39, 43)( 40, 42)( 47, 50)( 48, 49)
( 51, 56)( 52, 60)( 53, 59)( 54, 58)( 55, 57)( 62, 65)( 63, 64)( 66, 71)
( 67, 75)( 68, 74)( 69, 73)( 70, 72)( 77, 80)( 78, 79)( 81, 86)( 82, 90)
( 83, 89)( 84, 88)( 85, 87)( 92, 95)( 93, 94)( 96,101)( 97,105)( 98,104)
( 99,103)(100,102)(107,110)(108,109)(111,116)(112,120)(113,119)(114,118)
(115,117);
s1 := Sym(120)!(  1,  7)(  2,  6)(  3, 10)(  4,  9)(  5,  8)( 11, 12)( 13, 15)
( 16, 22)( 17, 21)( 18, 25)( 19, 24)( 20, 23)( 26, 27)( 28, 30)( 31, 52)
( 32, 51)( 33, 55)( 34, 54)( 35, 53)( 36, 47)( 37, 46)( 38, 50)( 39, 49)
( 40, 48)( 41, 57)( 42, 56)( 43, 60)( 44, 59)( 45, 58)( 61, 97)( 62, 96)
( 63,100)( 64, 99)( 65, 98)( 66, 92)( 67, 91)( 68, 95)( 69, 94)( 70, 93)
( 71,102)( 72,101)( 73,105)( 74,104)( 75,103)( 76,112)( 77,111)( 78,115)
( 79,114)( 80,113)( 81,107)( 82,106)( 83,110)( 84,109)( 85,108)( 86,117)
( 87,116)( 88,120)( 89,119)( 90,118);
s2 := Sym(120)!(  1, 61)(  2, 62)(  3, 63)(  4, 64)(  5, 65)(  6, 66)(  7, 67)
(  8, 68)(  9, 69)( 10, 70)( 11, 71)( 12, 72)( 13, 73)( 14, 74)( 15, 75)
( 16, 76)( 17, 77)( 18, 78)( 19, 79)( 20, 80)( 21, 81)( 22, 82)( 23, 83)
( 24, 84)( 25, 85)( 26, 86)( 27, 87)( 28, 88)( 29, 89)( 30, 90)( 31,106)
( 32,107)( 33,108)( 34,109)( 35,110)( 36,111)( 37,112)( 38,113)( 39,114)
( 40,115)( 41,116)( 42,117)( 43,118)( 44,119)( 45,120)( 46, 91)( 47, 92)
( 48, 93)( 49, 94)( 50, 95)( 51, 96)( 52, 97)( 53, 98)( 54, 99)( 55,100)
( 56,101)( 57,102)( 58,103)( 59,104)( 60,105);
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*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >; 
 
References : None.
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