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