Polytope of Type {2,12,20,2}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,12,20,2}*1920
if this polytope has a name.
Group : SmallGroup(1920,205047)
Rank : 5
Schlafli Type : {2,12,20,2}
Number of vertices, edges, etc : 2, 12, 120, 20, 2
Order of s0s1s2s3s4 : 60
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 : {2,12,10,2}*960, {2,6,20,2}*960a
3-fold quotients : {2,4,20,2}*640
4-fold quotients : {2,6,10,2}*480
5-fold quotients : {2,12,4,2}*384a
6-fold quotients : {2,2,20,2}*320, {2,4,10,2}*320
10-fold quotients : {2,12,2,2}*192, {2,6,4,2}*192a
12-fold quotients : {2,2,10,2}*160
15-fold quotients : {2,4,4,2}*128
20-fold quotients : {2,6,2,2}*96
24-fold quotients : {2,2,5,2}*80
30-fold quotients : {2,2,4,2}*64, {2,4,2,2}*64
40-fold quotients : {2,3,2,2}*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 := ( 8, 13)( 9, 14)( 10, 15)( 11, 16)( 12, 17)( 23, 28)( 24, 29)( 25, 30)
( 26, 31)( 27, 32)( 38, 43)( 39, 44)( 40, 45)( 41, 46)( 42, 47)( 53, 58)
( 54, 59)( 55, 60)( 56, 61)( 57, 62)( 63, 78)( 64, 79)( 65, 80)( 66, 81)
( 67, 82)( 68, 88)( 69, 89)( 70, 90)( 71, 91)( 72, 92)( 73, 83)( 74, 84)
( 75, 85)( 76, 86)( 77, 87)( 93,108)( 94,109)( 95,110)( 96,111)( 97,112)
( 98,118)( 99,119)(100,120)(101,121)(102,122)(103,113)(104,114)(105,115)
(106,116)(107,117);;
s2 := ( 3, 68)( 4, 72)( 5, 71)( 6, 70)( 7, 69)( 8, 63)( 9, 67)( 10, 66)
( 11, 65)( 12, 64)( 13, 73)( 14, 77)( 15, 76)( 16, 75)( 17, 74)( 18, 83)
( 19, 87)( 20, 86)( 21, 85)( 22, 84)( 23, 78)( 24, 82)( 25, 81)( 26, 80)
( 27, 79)( 28, 88)( 29, 92)( 30, 91)( 31, 90)( 32, 89)( 33, 98)( 34,102)
( 35,101)( 36,100)( 37, 99)( 38, 93)( 39, 97)( 40, 96)( 41, 95)( 42, 94)
( 43,103)( 44,107)( 45,106)( 46,105)( 47,104)( 48,113)( 49,117)( 50,116)
( 51,115)( 52,114)( 53,108)( 54,112)( 55,111)( 56,110)( 57,109)( 58,118)
( 59,122)( 60,121)( 61,120)( 62,119);;
s3 := ( 3, 4)( 5, 7)( 8, 9)( 10, 12)( 13, 14)( 15, 17)( 18, 19)( 20, 22)
( 23, 24)( 25, 27)( 28, 29)( 30, 32)( 33, 34)( 35, 37)( 38, 39)( 40, 42)
( 43, 44)( 45, 47)( 48, 49)( 50, 52)( 53, 54)( 55, 57)( 58, 59)( 60, 62)
( 63, 94)( 64, 93)( 65, 97)( 66, 96)( 67, 95)( 68, 99)( 69, 98)( 70,102)
( 71,101)( 72,100)( 73,104)( 74,103)( 75,107)( 76,106)( 77,105)( 78,109)
( 79,108)( 80,112)( 81,111)( 82,110)( 83,114)( 84,113)( 85,117)( 86,116)
( 87,115)( 88,119)( 89,118)( 90,122)( 91,121)( 92,120);;
s4 := (123,124);;
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, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s3*s4*s3*s4, s1*s2*s3*s2*s1*s2*s3*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
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)!( 8, 13)( 9, 14)( 10, 15)( 11, 16)( 12, 17)( 23, 28)( 24, 29)
( 25, 30)( 26, 31)( 27, 32)( 38, 43)( 39, 44)( 40, 45)( 41, 46)( 42, 47)
( 53, 58)( 54, 59)( 55, 60)( 56, 61)( 57, 62)( 63, 78)( 64, 79)( 65, 80)
( 66, 81)( 67, 82)( 68, 88)( 69, 89)( 70, 90)( 71, 91)( 72, 92)( 73, 83)
( 74, 84)( 75, 85)( 76, 86)( 77, 87)( 93,108)( 94,109)( 95,110)( 96,111)
( 97,112)( 98,118)( 99,119)(100,120)(101,121)(102,122)(103,113)(104,114)
(105,115)(106,116)(107,117);
s2 := Sym(124)!( 3, 68)( 4, 72)( 5, 71)( 6, 70)( 7, 69)( 8, 63)( 9, 67)
( 10, 66)( 11, 65)( 12, 64)( 13, 73)( 14, 77)( 15, 76)( 16, 75)( 17, 74)
( 18, 83)( 19, 87)( 20, 86)( 21, 85)( 22, 84)( 23, 78)( 24, 82)( 25, 81)
( 26, 80)( 27, 79)( 28, 88)( 29, 92)( 30, 91)( 31, 90)( 32, 89)( 33, 98)
( 34,102)( 35,101)( 36,100)( 37, 99)( 38, 93)( 39, 97)( 40, 96)( 41, 95)
( 42, 94)( 43,103)( 44,107)( 45,106)( 46,105)( 47,104)( 48,113)( 49,117)
( 50,116)( 51,115)( 52,114)( 53,108)( 54,112)( 55,111)( 56,110)( 57,109)
( 58,118)( 59,122)( 60,121)( 61,120)( 62,119);
s3 := Sym(124)!( 3, 4)( 5, 7)( 8, 9)( 10, 12)( 13, 14)( 15, 17)( 18, 19)
( 20, 22)( 23, 24)( 25, 27)( 28, 29)( 30, 32)( 33, 34)( 35, 37)( 38, 39)
( 40, 42)( 43, 44)( 45, 47)( 48, 49)( 50, 52)( 53, 54)( 55, 57)( 58, 59)
( 60, 62)( 63, 94)( 64, 93)( 65, 97)( 66, 96)( 67, 95)( 68, 99)( 69, 98)
( 70,102)( 71,101)( 72,100)( 73,104)( 74,103)( 75,107)( 76,106)( 77,105)
( 78,109)( 79,108)( 80,112)( 81,111)( 82,110)( 83,114)( 84,113)( 85,117)
( 86,116)( 87,115)( 88,119)( 89,118)( 90,122)( 91,121)( 92,120);
s4 := Sym(124)!(123,124);
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,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4,
s1*s2*s3*s2*s1*s2*s3*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
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