Polytope of Type {2,30,8,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,30,8,2}*1920
if this polytope has a name.
Group : SmallGroup(1920,235336)
Rank : 5
Schlafli Type : {2,30,8,2}
Number of vertices, edges, etc : 2, 30, 120, 8, 2
Order of s₀s₁s₂s₃s₄ : 120
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,30,4,2}*960a
   3-fold quotients : {2,10,8,2}*640
   4-fold quotients : {2,30,2,2}*480
   5-fold quotients : {2,6,8,2}*384
   6-fold quotients : {2,10,4,2}*320
   8-fold quotients : {2,15,2,2}*240
   10-fold quotients : {2,6,4,2}*192a
   12-fold quotients : {2,10,2,2}*160
   15-fold quotients : {2,2,8,2}*128
   20-fold quotients : {2,6,2,2}*96
   24-fold quotients : {2,5,2,2}*80
   30-fold quotients : {2,2,4,2}*64
   40-fold quotients : {2,3,2,2}*48
   60-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (  4,  7)(  5,  6)(  8, 13)(  9, 17)( 10, 16)( 11, 15)( 12, 14)( 19, 22)
( 20, 21)( 23, 28)( 24, 32)( 25, 31)( 26, 30)( 27, 29)( 34, 37)( 35, 36)
( 38, 43)( 39, 47)( 40, 46)( 41, 45)( 42, 44)( 49, 52)( 50, 51)( 53, 58)
( 54, 62)( 55, 61)( 56, 60)( 57, 59)( 64, 67)( 65, 66)( 68, 73)( 69, 77)
( 70, 76)( 71, 75)( 72, 74)( 79, 82)( 80, 81)( 83, 88)( 84, 92)( 85, 91)
( 86, 90)( 87, 89)( 94, 97)( 95, 96)( 98,103)( 99,107)(100,106)(101,105)
(102,104)(109,112)(110,111)(113,118)(114,122)(115,121)(116,120)(117,119);;
s2 := (  3,  9)(  4,  8)(  5, 12)(  6, 11)(  7, 10)( 13, 14)( 15, 17)( 18, 24)
( 19, 23)( 20, 27)( 21, 26)( 22, 25)( 28, 29)( 30, 32)( 33, 54)( 34, 53)
( 35, 57)( 36, 56)( 37, 55)( 38, 49)( 39, 48)( 40, 52)( 41, 51)( 42, 50)
( 43, 59)( 44, 58)( 45, 62)( 46, 61)( 47, 60)( 63, 99)( 64, 98)( 65,102)
( 66,101)( 67,100)( 68, 94)( 69, 93)( 70, 97)( 71, 96)( 72, 95)( 73,104)
( 74,103)( 75,107)( 76,106)( 77,105)( 78,114)( 79,113)( 80,117)( 81,116)
( 82,115)( 83,109)( 84,108)( 85,112)( 86,111)( 87,110)( 88,119)( 89,118)
( 90,122)( 91,121)( 92,120);;
s3 := (  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, 91)( 32, 92)( 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)( 46,121)( 47,122)( 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)( 61,106)( 62,107);;
s4 := (123,124);;
poly := Group([s0,s1,s2,s3,s4]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s3*s4*s3*s4, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
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*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(124)!(1,2);
s1 := Sym(124)!(  4,  7)(  5,  6)(  8, 13)(  9, 17)( 10, 16)( 11, 15)( 12, 14)
( 19, 22)( 20, 21)( 23, 28)( 24, 32)( 25, 31)( 26, 30)( 27, 29)( 34, 37)
( 35, 36)( 38, 43)( 39, 47)( 40, 46)( 41, 45)( 42, 44)( 49, 52)( 50, 51)
( 53, 58)( 54, 62)( 55, 61)( 56, 60)( 57, 59)( 64, 67)( 65, 66)( 68, 73)
( 69, 77)( 70, 76)( 71, 75)( 72, 74)( 79, 82)( 80, 81)( 83, 88)( 84, 92)
( 85, 91)( 86, 90)( 87, 89)( 94, 97)( 95, 96)( 98,103)( 99,107)(100,106)
(101,105)(102,104)(109,112)(110,111)(113,118)(114,122)(115,121)(116,120)
(117,119);
s2 := Sym(124)!(  3,  9)(  4,  8)(  5, 12)(  6, 11)(  7, 10)( 13, 14)( 15, 17)
( 18, 24)( 19, 23)( 20, 27)( 21, 26)( 22, 25)( 28, 29)( 30, 32)( 33, 54)
( 34, 53)( 35, 57)( 36, 56)( 37, 55)( 38, 49)( 39, 48)( 40, 52)( 41, 51)
( 42, 50)( 43, 59)( 44, 58)( 45, 62)( 46, 61)( 47, 60)( 63, 99)( 64, 98)
( 65,102)( 66,101)( 67,100)( 68, 94)( 69, 93)( 70, 97)( 71, 96)( 72, 95)
( 73,104)( 74,103)( 75,107)( 76,106)( 77,105)( 78,114)( 79,113)( 80,117)
( 81,116)( 82,115)( 83,109)( 84,108)( 85,112)( 86,111)( 87,110)( 88,119)
( 89,118)( 90,122)( 91,121)( 92,120);
s3 := Sym(124)!(  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, 91)( 32, 92)( 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)( 46,121)( 47,122)( 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)( 61,106)( 62,107);
s4 := Sym(124)!(123,124);
poly := sub<Sym(124)|s0,s1,s2,s3,s4>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
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*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 >;

to this polytope