Overview
- Group
- SmallGroup(1120,989)
- Rank
- 4
- Schläfli Type
- {28,10,2}
- Vertices, edges, …
- 28, 140, 10, 2
- Order of s0s1s2s3
- 140
- Order of s0s1s2s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Degenerate
- Universal
- Orientable
- Flat
Quotients maximal quotients in bold
2-fold
5-fold
7-fold
10-fold
14-fold
20-fold
28-fold
35-fold
70-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := ( 2, 7)( 3, 6)( 4, 5)( 9, 14)( 10, 13)( 11, 12)( 16, 21)( 17, 20)( 18, 19)( 23, 28)( 24, 27)( 25, 26)( 30, 35)( 31, 34)( 32, 33)( 37, 42)( 38, 41)( 39, 40)( 44, 49)( 45, 48)( 46, 47)( 51, 56)( 52, 55)( 53, 54)( 58, 63)( 59, 62)( 60, 61)( 65, 70)( 66, 69)( 67, 68)( 71,106)( 72,112)( 73,111)( 74,110)( 75,109)( 76,108)( 77,107)( 78,113)( 79,119)( 80,118)( 81,117)( 82,116)( 83,115)( 84,114)( 85,120)( 86,126)( 87,125)( 88,124)( 89,123)( 90,122)( 91,121)( 92,127)( 93,133)( 94,132)( 95,131)( 96,130)( 97,129)( 98,128)( 99,134)(100,140)(101,139)(102,138)(103,137)(104,136)(105,135);; s1 := ( 1, 72)( 2, 71)( 3, 77)( 4, 76)( 5, 75)( 6, 74)( 7, 73)( 8,100)( 9, 99)( 10,105)( 11,104)( 12,103)( 13,102)( 14,101)( 15, 93)( 16, 92)( 17, 98)( 18, 97)( 19, 96)( 20, 95)( 21, 94)( 22, 86)( 23, 85)( 24, 91)( 25, 90)( 26, 89)( 27, 88)( 28, 87)( 29, 79)( 30, 78)( 31, 84)( 32, 83)( 33, 82)( 34, 81)( 35, 80)( 36,107)( 37,106)( 38,112)( 39,111)( 40,110)( 41,109)( 42,108)( 43,135)( 44,134)( 45,140)( 46,139)( 47,138)( 48,137)( 49,136)( 50,128)( 51,127)( 52,133)( 53,132)( 54,131)( 55,130)( 56,129)( 57,121)( 58,120)( 59,126)( 60,125)( 61,124)( 62,123)( 63,122)( 64,114)( 65,113)( 66,119)( 67,118)( 68,117)( 69,116)( 70,115);; s2 := ( 1, 8)( 2, 9)( 3, 10)( 4, 11)( 5, 12)( 6, 13)( 7, 14)( 15, 29)( 16, 30)( 17, 31)( 18, 32)( 19, 33)( 20, 34)( 21, 35)( 36, 43)( 37, 44)( 38, 45)( 39, 46)( 40, 47)( 41, 48)( 42, 49)( 50, 64)( 51, 65)( 52, 66)( 53, 67)( 54, 68)( 55, 69)( 56, 70)( 71, 78)( 72, 79)( 73, 80)( 74, 81)( 75, 82)( 76, 83)( 77, 84)( 85, 99)( 86,100)( 87,101)( 88,102)( 89,103)( 90,104)( 91,105)(106,113)(107,114)(108,115)(109,116)(110,117)(111,118)(112,119)(120,134)(121,135)(122,136)(123,137)(124,138)(125,139)(126,140);; s3 := (141,142);; poly := Group([s0,s1,s2,s3]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3,
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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(142)!( 2, 7)( 3, 6)( 4, 5)( 9, 14)( 10, 13)( 11, 12)( 16, 21)( 17, 20)( 18, 19)( 23, 28)( 24, 27)( 25, 26)( 30, 35)( 31, 34)( 32, 33)( 37, 42)( 38, 41)( 39, 40)( 44, 49)( 45, 48)( 46, 47)( 51, 56)( 52, 55)( 53, 54)( 58, 63)( 59, 62)( 60, 61)( 65, 70)( 66, 69)( 67, 68)( 71,106)( 72,112)( 73,111)( 74,110)( 75,109)( 76,108)( 77,107)( 78,113)( 79,119)( 80,118)( 81,117)( 82,116)( 83,115)( 84,114)( 85,120)( 86,126)( 87,125)( 88,124)( 89,123)( 90,122)( 91,121)( 92,127)( 93,133)( 94,132)( 95,131)( 96,130)( 97,129)( 98,128)( 99,134)(100,140)(101,139)(102,138)(103,137)(104,136)(105,135); s1 := Sym(142)!( 1, 72)( 2, 71)( 3, 77)( 4, 76)( 5, 75)( 6, 74)( 7, 73)( 8,100)( 9, 99)( 10,105)( 11,104)( 12,103)( 13,102)( 14,101)( 15, 93)( 16, 92)( 17, 98)( 18, 97)( 19, 96)( 20, 95)( 21, 94)( 22, 86)( 23, 85)( 24, 91)( 25, 90)( 26, 89)( 27, 88)( 28, 87)( 29, 79)( 30, 78)( 31, 84)( 32, 83)( 33, 82)( 34, 81)( 35, 80)( 36,107)( 37,106)( 38,112)( 39,111)( 40,110)( 41,109)( 42,108)( 43,135)( 44,134)( 45,140)( 46,139)( 47,138)( 48,137)( 49,136)( 50,128)( 51,127)( 52,133)( 53,132)( 54,131)( 55,130)( 56,129)( 57,121)( 58,120)( 59,126)( 60,125)( 61,124)( 62,123)( 63,122)( 64,114)( 65,113)( 66,119)( 67,118)( 68,117)( 69,116)( 70,115); s2 := Sym(142)!( 1, 8)( 2, 9)( 3, 10)( 4, 11)( 5, 12)( 6, 13)( 7, 14)( 15, 29)( 16, 30)( 17, 31)( 18, 32)( 19, 33)( 20, 34)( 21, 35)( 36, 43)( 37, 44)( 38, 45)( 39, 46)( 40, 47)( 41, 48)( 42, 49)( 50, 64)( 51, 65)( 52, 66)( 53, 67)( 54, 68)( 55, 69)( 56, 70)( 71, 78)( 72, 79)( 73, 80)( 74, 81)( 75, 82)( 76, 83)( 77, 84)( 85, 99)( 86,100)( 87,101)( 88,102)( 89,103)( 90,104)( 91,105)(106,113)(107,114)(108,115)(109,116)(110,117)(111,118)(112,119)(120,134)(121,135)(122,136)(123,137)(124,138)(125,139)(126,140); s3 := Sym(142)!(141,142); poly := sub<Sym(142)|s0,s1,s2,s3>;
Finitely Presented Group Representation (Magma)
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;