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