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

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

Permutation Representation (Magma) :

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

to this polytope