Polytope of Type {4,2,4,30}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,2,4,30}*1920c
if this polytope has a name.
Group : SmallGroup(1920,240291)
Rank : 5
Schlafli Type : {4,2,4,30}
Number of vertices, edges, etc : 4, 4, 4, 60, 30
Order of s₀s₁s₂s₃s₄ : 60
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Non-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 : {4,2,4,15}*960, {2,2,4,30}*960c
   4-fold quotients : {2,2,4,15}*480
   5-fold quotients : {4,2,4,6}*384b
   10-fold quotients : {4,2,4,3}*192, {2,2,4,6}*192b
   20-fold quotients : {2,2,4,3}*96
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope