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