Polytope of Type {30,4,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {30,4,4}*960
Also Known As : {{30,4|2},{4,4|2}}. if this polytope has another name.
Group : SmallGroup(960,10542)
Rank : 4
Schlafli Type : {30,4,4}
Number of vertices, edges, etc : 30, 60, 8, 4
Order of s₀s₁s₂s₃ : 60
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {30,4,4,2} of size 1920
Vertex Figure Of :
   {2,30,4,4} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {30,2,4}*480, {30,4,2}*480a
   3-fold quotients : {10,4,4}*320
   4-fold quotients : {15,2,4}*240, {30,2,2}*240
   5-fold quotients : {6,4,4}*192
   6-fold quotients : {10,2,4}*160, {10,4,2}*160
   8-fold quotients : {15,2,2}*120
   10-fold quotients : {6,2,4}*96, {6,4,2}*96a
   12-fold quotients : {5,2,4}*80, {10,2,2}*80
   15-fold quotients : {2,4,4}*64
   20-fold quotients : {3,2,4}*48, {6,2,2}*48
   24-fold quotients : {5,2,2}*40
   30-fold quotients : {2,2,4}*32, {2,4,2}*32
   40-fold quotients : {3,2,2}*24
   60-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {60,4,4}*1920, {30,4,8}*1920a, {30,8,4}*1920a, {30,4,8}*1920b, {30,8,4}*1920b, {30,4,4}*1920a
Permutation Representation (GAP) :

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

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

Finitely Presented Group Representation (Magma) :

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

References : None.
to this polytope