Polytope of Type {2,10,6,4,2}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,10,6,4,2}*1920b
if this polytope has a name.
Group : SmallGroup(1920,240407)
Rank : 6
Schlafli Type : {2,10,6,4,2}
Number of vertices, edges, etc : 2, 10, 30, 12, 4, 2
Order of s0s1s2s3s4s5 : 30
Order of s0s1s2s3s4s5s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Non-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) :
5-fold quotients : {2,2,6,4,2}*384c
10-fold quotients : {2,2,3,4,2}*192
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 7, 19)( 8, 20)( 9, 21)( 10, 22)( 11, 15)( 12, 16)( 13, 17)( 14, 18)
( 27, 39)( 28, 40)( 29, 41)( 30, 42)( 31, 35)( 32, 36)( 33, 37)( 34, 38)
( 47, 59)( 48, 60)( 49, 61)( 50, 62)( 51, 55)( 52, 56)( 53, 57)( 54, 58)
( 67, 79)( 68, 80)( 69, 81)( 70, 82)( 71, 75)( 72, 76)( 73, 77)( 74, 78)
( 87, 99)( 88,100)( 89,101)( 90,102)( 91, 95)( 92, 96)( 93, 97)( 94, 98)
(107,119)(108,120)(109,121)(110,122)(111,115)(112,116)(113,117)(114,118);;
s2 := ( 3, 7)( 4, 9)( 5, 8)( 6, 10)( 11, 19)( 12, 21)( 13, 20)( 14, 22)
( 16, 17)( 23, 47)( 24, 49)( 25, 48)( 26, 50)( 27, 43)( 28, 45)( 29, 44)
( 30, 46)( 31, 59)( 32, 61)( 33, 60)( 34, 62)( 35, 55)( 36, 57)( 37, 56)
( 38, 58)( 39, 51)( 40, 53)( 41, 52)( 42, 54)( 63, 67)( 64, 69)( 65, 68)
( 66, 70)( 71, 79)( 72, 81)( 73, 80)( 74, 82)( 76, 77)( 83,107)( 84,109)
( 85,108)( 86,110)( 87,103)( 88,105)( 89,104)( 90,106)( 91,119)( 92,121)
( 93,120)( 94,122)( 95,115)( 96,117)( 97,116)( 98,118)( 99,111)(100,113)
(101,112)(102,114);;
s3 := ( 3, 83)( 4, 84)( 5, 86)( 6, 85)( 7, 87)( 8, 88)( 9, 90)( 10, 89)
( 11, 91)( 12, 92)( 13, 94)( 14, 93)( 15, 95)( 16, 96)( 17, 98)( 18, 97)
( 19, 99)( 20,100)( 21,102)( 22,101)( 23, 63)( 24, 64)( 25, 66)( 26, 65)
( 27, 67)( 28, 68)( 29, 70)( 30, 69)( 31, 71)( 32, 72)( 33, 74)( 34, 73)
( 35, 75)( 36, 76)( 37, 78)( 38, 77)( 39, 79)( 40, 80)( 41, 82)( 42, 81)
( 43,103)( 44,104)( 45,106)( 46,105)( 47,107)( 48,108)( 49,110)( 50,109)
( 51,111)( 52,112)( 53,114)( 54,113)( 55,115)( 56,116)( 57,118)( 58,117)
( 59,119)( 60,120)( 61,122)( 62,121);;
s4 := ( 3, 6)( 4, 5)( 7, 10)( 8, 9)( 11, 14)( 12, 13)( 15, 18)( 16, 17)
( 19, 22)( 20, 21)( 23, 26)( 24, 25)( 27, 30)( 28, 29)( 31, 34)( 32, 33)
( 35, 38)( 36, 37)( 39, 42)( 40, 41)( 43, 46)( 44, 45)( 47, 50)( 48, 49)
( 51, 54)( 52, 53)( 55, 58)( 56, 57)( 59, 62)( 60, 61)( 63, 66)( 64, 65)
( 67, 70)( 68, 69)( 71, 74)( 72, 73)( 75, 78)( 76, 77)( 79, 82)( 80, 81)
( 83, 86)( 84, 85)( 87, 90)( 88, 89)( 91, 94)( 92, 93)( 95, 98)( 96, 97)
( 99,102)(100,101)(103,106)(104,105)(107,110)(108,109)(111,114)(112,113)
(115,118)(116,117)(119,122)(120,121);;
s5 := (123,124);;
poly := Group([s0,s1,s2,s3,s4,s5]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;; s5 := F.6;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5,
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, s0*s5*s0*s5, s1*s5*s1*s5,
s2*s5*s2*s5, s3*s5*s3*s5, s4*s5*s4*s5,
s1*s2*s3*s2*s1*s2*s3*s2, s3*s4*s3*s4*s3*s4*s3*s4,
s4*s3*s2*s4*s3*s4*s3*s2*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
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(124)!(1,2);
s1 := Sym(124)!( 7, 19)( 8, 20)( 9, 21)( 10, 22)( 11, 15)( 12, 16)( 13, 17)
( 14, 18)( 27, 39)( 28, 40)( 29, 41)( 30, 42)( 31, 35)( 32, 36)( 33, 37)
( 34, 38)( 47, 59)( 48, 60)( 49, 61)( 50, 62)( 51, 55)( 52, 56)( 53, 57)
( 54, 58)( 67, 79)( 68, 80)( 69, 81)( 70, 82)( 71, 75)( 72, 76)( 73, 77)
( 74, 78)( 87, 99)( 88,100)( 89,101)( 90,102)( 91, 95)( 92, 96)( 93, 97)
( 94, 98)(107,119)(108,120)(109,121)(110,122)(111,115)(112,116)(113,117)
(114,118);
s2 := Sym(124)!( 3, 7)( 4, 9)( 5, 8)( 6, 10)( 11, 19)( 12, 21)( 13, 20)
( 14, 22)( 16, 17)( 23, 47)( 24, 49)( 25, 48)( 26, 50)( 27, 43)( 28, 45)
( 29, 44)( 30, 46)( 31, 59)( 32, 61)( 33, 60)( 34, 62)( 35, 55)( 36, 57)
( 37, 56)( 38, 58)( 39, 51)( 40, 53)( 41, 52)( 42, 54)( 63, 67)( 64, 69)
( 65, 68)( 66, 70)( 71, 79)( 72, 81)( 73, 80)( 74, 82)( 76, 77)( 83,107)
( 84,109)( 85,108)( 86,110)( 87,103)( 88,105)( 89,104)( 90,106)( 91,119)
( 92,121)( 93,120)( 94,122)( 95,115)( 96,117)( 97,116)( 98,118)( 99,111)
(100,113)(101,112)(102,114);
s3 := Sym(124)!( 3, 83)( 4, 84)( 5, 86)( 6, 85)( 7, 87)( 8, 88)( 9, 90)
( 10, 89)( 11, 91)( 12, 92)( 13, 94)( 14, 93)( 15, 95)( 16, 96)( 17, 98)
( 18, 97)( 19, 99)( 20,100)( 21,102)( 22,101)( 23, 63)( 24, 64)( 25, 66)
( 26, 65)( 27, 67)( 28, 68)( 29, 70)( 30, 69)( 31, 71)( 32, 72)( 33, 74)
( 34, 73)( 35, 75)( 36, 76)( 37, 78)( 38, 77)( 39, 79)( 40, 80)( 41, 82)
( 42, 81)( 43,103)( 44,104)( 45,106)( 46,105)( 47,107)( 48,108)( 49,110)
( 50,109)( 51,111)( 52,112)( 53,114)( 54,113)( 55,115)( 56,116)( 57,118)
( 58,117)( 59,119)( 60,120)( 61,122)( 62,121);
s4 := Sym(124)!( 3, 6)( 4, 5)( 7, 10)( 8, 9)( 11, 14)( 12, 13)( 15, 18)
( 16, 17)( 19, 22)( 20, 21)( 23, 26)( 24, 25)( 27, 30)( 28, 29)( 31, 34)
( 32, 33)( 35, 38)( 36, 37)( 39, 42)( 40, 41)( 43, 46)( 44, 45)( 47, 50)
( 48, 49)( 51, 54)( 52, 53)( 55, 58)( 56, 57)( 59, 62)( 60, 61)( 63, 66)
( 64, 65)( 67, 70)( 68, 69)( 71, 74)( 72, 73)( 75, 78)( 76, 77)( 79, 82)
( 80, 81)( 83, 86)( 84, 85)( 87, 90)( 88, 89)( 91, 94)( 92, 93)( 95, 98)
( 96, 97)( 99,102)(100,101)(103,106)(104,105)(107,110)(108,109)(111,114)
(112,113)(115,118)(116,117)(119,122)(120,121);
s5 := Sym(124)!(123,124);
poly := sub<Sym(124)|s0,s1,s2,s3,s4,s5>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s5*s5, 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, s0*s5*s0*s5,
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5,
s4*s5*s4*s5, s1*s2*s3*s2*s1*s2*s3*s2,
s3*s4*s3*s4*s3*s4*s3*s4, s4*s3*s2*s4*s3*s4*s3*s2*s3,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
to this polytope