Polytope of Type {3,2,4,15}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,4,15}*1440
if this polytope has a name.
Group : SmallGroup(1440,5900)
Rank : 5
Schlafli Type : {3,2,4,15}
Number of vertices, edges, etc : 3, 3, 8, 60, 30
Order of s₀s₁s₂s₃s₄ : 30
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 : {3,2,4,15}*720
   4-fold quotients : {3,2,2,15}*360
   5-fold quotients : {3,2,4,3}*288
   10-fold quotients : {3,2,4,3}*144
   12-fold quotients : {3,2,2,5}*120
   20-fold quotients : {3,2,2,3}*72
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope