Polytope of Type {2,2,12,20}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,12,20}*1920
if this polytope has a name.
Group : SmallGroup(1920,205047)
Rank : 5
Schlafli Type : {2,2,12,20}
Number of vertices, edges, etc : 2, 2, 12, 120, 20
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 : {2,2,12,10}*960, {2,2,6,20}*960a
3-fold quotients : {2,2,4,20}*640
4-fold quotients : {2,2,6,10}*480
5-fold quotients : {2,2,12,4}*384a
6-fold quotients : {2,2,2,20}*320, {2,2,4,10}*320
10-fold quotients : {2,2,12,2}*192, {2,2,6,4}*192a
12-fold quotients : {2,2,2,10}*160
15-fold quotients : {2,2,4,4}*128
20-fold quotients : {2,2,6,2}*96
24-fold quotients : {2,2,2,5}*80
30-fold quotients : {2,2,2,4}*64, {2,2,4,2}*64
40-fold quotients : {2,2,3,2}*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 := (3,4);;
s2 := ( 10, 15)( 11, 16)( 12, 17)( 13, 18)( 14, 19)( 25, 30)( 26, 31)( 27, 32)
( 28, 33)( 29, 34)( 40, 45)( 41, 46)( 42, 47)( 43, 48)( 44, 49)( 55, 60)
( 56, 61)( 57, 62)( 58, 63)( 59, 64)( 65, 80)( 66, 81)( 67, 82)( 68, 83)
( 69, 84)( 70, 90)( 71, 91)( 72, 92)( 73, 93)( 74, 94)( 75, 85)( 76, 86)
( 77, 87)( 78, 88)( 79, 89)( 95,110)( 96,111)( 97,112)( 98,113)( 99,114)
(100,120)(101,121)(102,122)(103,123)(104,124)(105,115)(106,116)(107,117)
(108,118)(109,119);;
s3 := ( 5, 70)( 6, 74)( 7, 73)( 8, 72)( 9, 71)( 10, 65)( 11, 69)( 12, 68)
( 13, 67)( 14, 66)( 15, 75)( 16, 79)( 17, 78)( 18, 77)( 19, 76)( 20, 85)
( 21, 89)( 22, 88)( 23, 87)( 24, 86)( 25, 80)( 26, 84)( 27, 83)( 28, 82)
( 29, 81)( 30, 90)( 31, 94)( 32, 93)( 33, 92)( 34, 91)( 35,100)( 36,104)
( 37,103)( 38,102)( 39,101)( 40, 95)( 41, 99)( 42, 98)( 43, 97)( 44, 96)
( 45,105)( 46,109)( 47,108)( 48,107)( 49,106)( 50,115)( 51,119)( 52,118)
( 53,117)( 54,116)( 55,110)( 56,114)( 57,113)( 58,112)( 59,111)( 60,120)
( 61,124)( 62,123)( 63,122)( 64,121);;
s4 := ( 5, 6)( 7, 9)( 10, 11)( 12, 14)( 15, 16)( 17, 19)( 20, 21)( 22, 24)
( 25, 26)( 27, 29)( 30, 31)( 32, 34)( 35, 36)( 37, 39)( 40, 41)( 42, 44)
( 45, 46)( 47, 49)( 50, 51)( 52, 54)( 55, 56)( 57, 59)( 60, 61)( 62, 64)
( 65, 96)( 66, 95)( 67, 99)( 68, 98)( 69, 97)( 70,101)( 71,100)( 72,104)
( 73,103)( 74,102)( 75,106)( 76,105)( 77,109)( 78,108)( 79,107)( 80,111)
( 81,110)( 82,114)( 83,113)( 84,112)( 85,116)( 86,115)( 87,119)( 88,118)
( 89,117)( 90,121)( 91,120)( 92,124)( 93,123)( 94,122);;
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*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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(124)!(1,2);
s1 := Sym(124)!(3,4);
s2 := Sym(124)!( 10, 15)( 11, 16)( 12, 17)( 13, 18)( 14, 19)( 25, 30)( 26, 31)
( 27, 32)( 28, 33)( 29, 34)( 40, 45)( 41, 46)( 42, 47)( 43, 48)( 44, 49)
( 55, 60)( 56, 61)( 57, 62)( 58, 63)( 59, 64)( 65, 80)( 66, 81)( 67, 82)
( 68, 83)( 69, 84)( 70, 90)( 71, 91)( 72, 92)( 73, 93)( 74, 94)( 75, 85)
( 76, 86)( 77, 87)( 78, 88)( 79, 89)( 95,110)( 96,111)( 97,112)( 98,113)
( 99,114)(100,120)(101,121)(102,122)(103,123)(104,124)(105,115)(106,116)
(107,117)(108,118)(109,119);
s3 := Sym(124)!( 5, 70)( 6, 74)( 7, 73)( 8, 72)( 9, 71)( 10, 65)( 11, 69)
( 12, 68)( 13, 67)( 14, 66)( 15, 75)( 16, 79)( 17, 78)( 18, 77)( 19, 76)
( 20, 85)( 21, 89)( 22, 88)( 23, 87)( 24, 86)( 25, 80)( 26, 84)( 27, 83)
( 28, 82)( 29, 81)( 30, 90)( 31, 94)( 32, 93)( 33, 92)( 34, 91)( 35,100)
( 36,104)( 37,103)( 38,102)( 39,101)( 40, 95)( 41, 99)( 42, 98)( 43, 97)
( 44, 96)( 45,105)( 46,109)( 47,108)( 48,107)( 49,106)( 50,115)( 51,119)
( 52,118)( 53,117)( 54,116)( 55,110)( 56,114)( 57,113)( 58,112)( 59,111)
( 60,120)( 61,124)( 62,123)( 63,122)( 64,121);
s4 := Sym(124)!( 5, 6)( 7, 9)( 10, 11)( 12, 14)( 15, 16)( 17, 19)( 20, 21)
( 22, 24)( 25, 26)( 27, 29)( 30, 31)( 32, 34)( 35, 36)( 37, 39)( 40, 41)
( 42, 44)( 45, 46)( 47, 49)( 50, 51)( 52, 54)( 55, 56)( 57, 59)( 60, 61)
( 62, 64)( 65, 96)( 66, 95)( 67, 99)( 68, 98)( 69, 97)( 70,101)( 71,100)
( 72,104)( 73,103)( 74,102)( 75,106)( 76,105)( 77,109)( 78,108)( 79,107)
( 80,111)( 81,110)( 82,114)( 83,113)( 84,112)( 85,116)( 86,115)( 87,119)
( 88,118)( 89,117)( 90,121)( 91,120)( 92,124)( 93,123)( 94,122);
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*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 >;
to this polytope