Polytope of Type {2,12,4,10}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,12,4,10}*1920
if this polytope has a name.
Group : SmallGroup(1920,205032)
Rank : 5
Schlafli Type : {2,12,4,10}
Number of vertices, edges, etc : 2, 12, 24, 20, 10
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 : {2,12,2,10}*960, {2,6,4,10}*960
3-fold quotients : {2,4,4,10}*640
4-fold quotients : {2,12,2,5}*480, {2,6,2,10}*480
5-fold quotients : {2,12,4,2}*384a
6-fold quotients : {2,2,4,10}*320, {2,4,2,10}*320
8-fold quotients : {2,3,2,10}*240, {2,6,2,5}*240
10-fold quotients : {2,12,2,2}*192, {2,6,4,2}*192a
12-fold quotients : {2,4,2,5}*160, {2,2,2,10}*160
15-fold quotients : {2,4,4,2}*128
16-fold quotients : {2,3,2,5}*120
20-fold quotients : {2,6,2,2}*96
24-fold quotients : {2,2,2,5}*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, 93)( 64, 94)( 65, 95)( 66, 96)
( 67, 97)( 68,103)( 69,104)( 70,105)( 71,106)( 72,107)( 73, 98)( 74, 99)
( 75,100)( 76,101)( 77,102)( 78,108)( 79,109)( 80,110)( 81,111)( 82,112)
( 83,118)( 84,119)( 85,120)( 86,121)( 87,122)( 88,113)( 89,114)( 90,115)
( 91,116)( 92,117);;
s2 := ( 3, 68)( 4, 69)( 5, 70)( 6, 71)( 7, 72)( 8, 63)( 9, 64)( 10, 65)
( 11, 66)( 12, 67)( 13, 73)( 14, 74)( 15, 75)( 16, 76)( 17, 77)( 18, 83)
( 19, 84)( 20, 85)( 21, 86)( 22, 87)( 23, 78)( 24, 79)( 25, 80)( 26, 81)
( 27, 82)( 28, 88)( 29, 89)( 30, 90)( 31, 91)( 32, 92)( 33, 98)( 34, 99)
( 35,100)( 36,101)( 37,102)( 38, 93)( 39, 94)( 40, 95)( 41, 96)( 42, 97)
( 43,103)( 44,104)( 45,105)( 46,106)( 47,107)( 48,113)( 49,114)( 50,115)
( 51,116)( 52,117)( 53,108)( 54,109)( 55,110)( 56,111)( 57,112)( 58,118)
( 59,119)( 60,120)( 61,121)( 62,122);;
s3 := ( 4, 7)( 5, 6)( 9, 12)( 10, 11)( 14, 17)( 15, 16)( 19, 22)( 20, 21)
( 24, 27)( 25, 26)( 29, 32)( 30, 31)( 34, 37)( 35, 36)( 39, 42)( 40, 41)
( 44, 47)( 45, 46)( 49, 52)( 50, 51)( 54, 57)( 55, 56)( 59, 62)( 60, 61)
( 63, 78)( 64, 82)( 65, 81)( 66, 80)( 67, 79)( 68, 83)( 69, 87)( 70, 86)
( 71, 85)( 72, 84)( 73, 88)( 74, 92)( 75, 91)( 76, 90)( 77, 89)( 93,108)
( 94,112)( 95,111)( 96,110)( 97,109)( 98,113)( 99,117)(100,116)(101,115)
(102,114)(103,118)(104,122)(105,121)(106,120)(107,119);;
s4 := ( 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, 64)( 65, 67)( 68, 69)( 70, 72)( 73, 74)( 75, 77)( 78, 79)( 80, 82)
( 83, 84)( 85, 87)( 88, 89)( 90, 92)( 93, 94)( 95, 97)( 98, 99)(100,102)
(103,104)(105,107)(108,109)(110,112)(113,114)(115,117)(118,119)(120,122);;
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, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3,
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(122)!(1,2);
s1 := Sym(122)!( 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, 93)( 64, 94)( 65, 95)
( 66, 96)( 67, 97)( 68,103)( 69,104)( 70,105)( 71,106)( 72,107)( 73, 98)
( 74, 99)( 75,100)( 76,101)( 77,102)( 78,108)( 79,109)( 80,110)( 81,111)
( 82,112)( 83,118)( 84,119)( 85,120)( 86,121)( 87,122)( 88,113)( 89,114)
( 90,115)( 91,116)( 92,117);
s2 := Sym(122)!( 3, 68)( 4, 69)( 5, 70)( 6, 71)( 7, 72)( 8, 63)( 9, 64)
( 10, 65)( 11, 66)( 12, 67)( 13, 73)( 14, 74)( 15, 75)( 16, 76)( 17, 77)
( 18, 83)( 19, 84)( 20, 85)( 21, 86)( 22, 87)( 23, 78)( 24, 79)( 25, 80)
( 26, 81)( 27, 82)( 28, 88)( 29, 89)( 30, 90)( 31, 91)( 32, 92)( 33, 98)
( 34, 99)( 35,100)( 36,101)( 37,102)( 38, 93)( 39, 94)( 40, 95)( 41, 96)
( 42, 97)( 43,103)( 44,104)( 45,105)( 46,106)( 47,107)( 48,113)( 49,114)
( 50,115)( 51,116)( 52,117)( 53,108)( 54,109)( 55,110)( 56,111)( 57,112)
( 58,118)( 59,119)( 60,120)( 61,121)( 62,122);
s3 := Sym(122)!( 4, 7)( 5, 6)( 9, 12)( 10, 11)( 14, 17)( 15, 16)( 19, 22)
( 20, 21)( 24, 27)( 25, 26)( 29, 32)( 30, 31)( 34, 37)( 35, 36)( 39, 42)
( 40, 41)( 44, 47)( 45, 46)( 49, 52)( 50, 51)( 54, 57)( 55, 56)( 59, 62)
( 60, 61)( 63, 78)( 64, 82)( 65, 81)( 66, 80)( 67, 79)( 68, 83)( 69, 87)
( 70, 86)( 71, 85)( 72, 84)( 73, 88)( 74, 92)( 75, 91)( 76, 90)( 77, 89)
( 93,108)( 94,112)( 95,111)( 96,110)( 97,109)( 98,113)( 99,117)(100,116)
(101,115)(102,114)(103,118)(104,122)(105,121)(106,120)(107,119);
s4 := Sym(122)!( 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, 64)( 65, 67)( 68, 69)( 70, 72)( 73, 74)( 75, 77)( 78, 79)
( 80, 82)( 83, 84)( 85, 87)( 88, 89)( 90, 92)( 93, 94)( 95, 97)( 98, 99)
(100,102)(103,104)(105,107)(108,109)(110,112)(113,114)(115,117)(118,119)
(120,122);
poly := sub<Sym(122)|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, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*s3,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
to this polytope