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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,30,8}*1920
if this polytope has a name.
Group : SmallGroup(1920,235336)
Rank : 5
Schlafli Type : {2,2,30,8}
Number of vertices, edges, etc : 2, 2, 30, 120, 8
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 : {2,2,30,4}*960a
   3-fold quotients : {2,2,10,8}*640
   4-fold quotients : {2,2,30,2}*480
   5-fold quotients : {2,2,6,8}*384
   6-fold quotients : {2,2,10,4}*320
   8-fold quotients : {2,2,15,2}*240
   10-fold quotients : {2,2,6,4}*192a
   12-fold quotients : {2,2,10,2}*160
   15-fold quotients : {2,2,2,8}*128
   20-fold quotients : {2,2,6,2}*96
   24-fold quotients : {2,2,5,2}*80
   30-fold quotients : {2,2,2,4}*64
   40-fold quotients : {2,2,3,2}*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 := (3,4);;
s2 := (  6,  9)(  7,  8)( 10, 15)( 11, 19)( 12, 18)( 13, 17)( 14, 16)( 21, 24)
( 22, 23)( 25, 30)( 26, 34)( 27, 33)( 28, 32)( 29, 31)( 36, 39)( 37, 38)
( 40, 45)( 41, 49)( 42, 48)( 43, 47)( 44, 46)( 51, 54)( 52, 53)( 55, 60)
( 56, 64)( 57, 63)( 58, 62)( 59, 61)( 66, 69)( 67, 68)( 70, 75)( 71, 79)
( 72, 78)( 73, 77)( 74, 76)( 81, 84)( 82, 83)( 85, 90)( 86, 94)( 87, 93)
( 88, 92)( 89, 91)( 96, 99)( 97, 98)(100,105)(101,109)(102,108)(103,107)
(104,106)(111,114)(112,113)(115,120)(116,124)(117,123)(118,122)(119,121);;
s3 := (  5, 11)(  6, 10)(  7, 14)(  8, 13)(  9, 12)( 15, 16)( 17, 19)( 20, 26)
( 21, 25)( 22, 29)( 23, 28)( 24, 27)( 30, 31)( 32, 34)( 35, 56)( 36, 55)
( 37, 59)( 38, 58)( 39, 57)( 40, 51)( 41, 50)( 42, 54)( 43, 53)( 44, 52)
( 45, 61)( 46, 60)( 47, 64)( 48, 63)( 49, 62)( 65,101)( 66,100)( 67,104)
( 68,103)( 69,102)( 70, 96)( 71, 95)( 72, 99)( 73, 98)( 74, 97)( 75,106)
( 76,105)( 77,109)( 78,108)( 79,107)( 80,116)( 81,115)( 82,119)( 83,118)
( 84,117)( 85,111)( 86,110)( 87,114)( 88,113)( 89,112)( 90,121)( 91,120)
( 92,124)( 93,123)( 94,122);;
s4 := (  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, 93)( 34, 94)( 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)( 48,123)( 49,124)( 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)( 63,108)( 64,109);;
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, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s2*s3*s4*s3*s2*s3*s4*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

to this polytope