Overview
- Group
- SmallGroup(1120,1061)
- Rank
- 4
- Schläfli Type
- {2,70,4}
- Vertices, edges, …
- 2, 70, 140, 4
- 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
4-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 := (1,2);; s1 := ( 4, 9)( 5, 8)( 6, 7)( 10, 31)( 11, 37)( 12, 36)( 13, 35)( 14, 34)( 15, 33)( 16, 32)( 17, 24)( 18, 30)( 19, 29)( 20, 28)( 21, 27)( 22, 26)( 23, 25)( 39, 44)( 40, 43)( 41, 42)( 45, 66)( 46, 72)( 47, 71)( 48, 70)( 49, 69)( 50, 68)( 51, 67)( 52, 59)( 53, 65)( 54, 64)( 55, 63)( 56, 62)( 57, 61)( 58, 60)( 74, 79)( 75, 78)( 76, 77)( 80,101)( 81,107)( 82,106)( 83,105)( 84,104)( 85,103)( 86,102)( 87, 94)( 88,100)( 89, 99)( 90, 98)( 91, 97)( 92, 96)( 93, 95)(109,114)(110,113)(111,112)(115,136)(116,142)(117,141)(118,140)(119,139)(120,138)(121,137)(122,129)(123,135)(124,134)(125,133)(126,132)(127,131)(128,130);; s2 := ( 3, 11)( 4, 10)( 5, 16)( 6, 15)( 7, 14)( 8, 13)( 9, 12)( 17, 32)( 18, 31)( 19, 37)( 20, 36)( 21, 35)( 22, 34)( 23, 33)( 24, 25)( 26, 30)( 27, 29)( 38, 46)( 39, 45)( 40, 51)( 41, 50)( 42, 49)( 43, 48)( 44, 47)( 52, 67)( 53, 66)( 54, 72)( 55, 71)( 56, 70)( 57, 69)( 58, 68)( 59, 60)( 61, 65)( 62, 64)( 73,116)( 74,115)( 75,121)( 76,120)( 77,119)( 78,118)( 79,117)( 80,109)( 81,108)( 82,114)( 83,113)( 84,112)( 85,111)( 86,110)( 87,137)( 88,136)( 89,142)( 90,141)( 91,140)( 92,139)( 93,138)( 94,130)( 95,129)( 96,135)( 97,134)( 98,133)( 99,132)(100,131)(101,123)(102,122)(103,128)(104,127)(105,126)(106,125)(107,124);; s3 := ( 3, 73)( 4, 74)( 5, 75)( 6, 76)( 7, 77)( 8, 78)( 9, 79)( 10, 80)( 11, 81)( 12, 82)( 13, 83)( 14, 84)( 15, 85)( 16, 86)( 17, 87)( 18, 88)( 19, 89)( 20, 90)( 21, 91)( 22, 92)( 23, 93)( 24, 94)( 25, 95)( 26, 96)( 27, 97)( 28, 98)( 29, 99)( 30,100)( 31,101)( 32,102)( 33,103)( 34,104)( 35,105)( 36,106)( 37,107)( 38,108)( 39,109)( 40,110)( 41,111)( 42,112)( 43,113)( 44,114)( 45,115)( 46,116)( 47,117)( 48,118)( 49,119)( 50,120)( 51,121)( 52,122)( 53,123)( 54,124)( 55,125)( 56,126)( 57,127)( 58,128)( 59,129)( 60,130)( 61,131)( 62,132)( 63,133)( 64,134)( 65,135)( 66,136)( 67,137)( 68,138)( 69,139)( 70,140)( 71,141)( 72,142);; 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*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s1*s2*s3*s2*s1*s2*s3*s2, 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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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(142)!(1,2); s1 := Sym(142)!( 4, 9)( 5, 8)( 6, 7)( 10, 31)( 11, 37)( 12, 36)( 13, 35)( 14, 34)( 15, 33)( 16, 32)( 17, 24)( 18, 30)( 19, 29)( 20, 28)( 21, 27)( 22, 26)( 23, 25)( 39, 44)( 40, 43)( 41, 42)( 45, 66)( 46, 72)( 47, 71)( 48, 70)( 49, 69)( 50, 68)( 51, 67)( 52, 59)( 53, 65)( 54, 64)( 55, 63)( 56, 62)( 57, 61)( 58, 60)( 74, 79)( 75, 78)( 76, 77)( 80,101)( 81,107)( 82,106)( 83,105)( 84,104)( 85,103)( 86,102)( 87, 94)( 88,100)( 89, 99)( 90, 98)( 91, 97)( 92, 96)( 93, 95)(109,114)(110,113)(111,112)(115,136)(116,142)(117,141)(118,140)(119,139)(120,138)(121,137)(122,129)(123,135)(124,134)(125,133)(126,132)(127,131)(128,130); s2 := Sym(142)!( 3, 11)( 4, 10)( 5, 16)( 6, 15)( 7, 14)( 8, 13)( 9, 12)( 17, 32)( 18, 31)( 19, 37)( 20, 36)( 21, 35)( 22, 34)( 23, 33)( 24, 25)( 26, 30)( 27, 29)( 38, 46)( 39, 45)( 40, 51)( 41, 50)( 42, 49)( 43, 48)( 44, 47)( 52, 67)( 53, 66)( 54, 72)( 55, 71)( 56, 70)( 57, 69)( 58, 68)( 59, 60)( 61, 65)( 62, 64)( 73,116)( 74,115)( 75,121)( 76,120)( 77,119)( 78,118)( 79,117)( 80,109)( 81,108)( 82,114)( 83,113)( 84,112)( 85,111)( 86,110)( 87,137)( 88,136)( 89,142)( 90,141)( 91,140)( 92,139)( 93,138)( 94,130)( 95,129)( 96,135)( 97,134)( 98,133)( 99,132)(100,131)(101,123)(102,122)(103,128)(104,127)(105,126)(106,125)(107,124); s3 := Sym(142)!( 3, 73)( 4, 74)( 5, 75)( 6, 76)( 7, 77)( 8, 78)( 9, 79)( 10, 80)( 11, 81)( 12, 82)( 13, 83)( 14, 84)( 15, 85)( 16, 86)( 17, 87)( 18, 88)( 19, 89)( 20, 90)( 21, 91)( 22, 92)( 23, 93)( 24, 94)( 25, 95)( 26, 96)( 27, 97)( 28, 98)( 29, 99)( 30,100)( 31,101)( 32,102)( 33,103)( 34,104)( 35,105)( 36,106)( 37,107)( 38,108)( 39,109)( 40,110)( 41,111)( 42,112)( 43,113)( 44,114)( 45,115)( 46,116)( 47,117)( 48,118)( 49,119)( 50,120)( 51,121)( 52,122)( 53,123)( 54,124)( 55,125)( 56,126)( 57,127)( 58,128)( 59,129)( 60,130)( 61,131)( 62,132)( 63,133)( 64,134)( 65,135)( 66,136)( 67,137)( 68,138)( 69,139)( 70,140)( 71,141)( 72,142); 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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, s1*s2*s3*s2*s1*s2*s3*s2, 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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;