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