Overview
- Group
- SmallGroup(1120,998)
- Rank
- 4
- Schläfli Type
- {4,10,14}
- Vertices, edges, …
- 4, 20, 70, 14
- Order of s0s1s2s3
- 140
- Order of s0s1s2s3s2s1
- 2
- Also known as
- {{4,10|2},{10,14|2}}. if this polytope has another name.
Special Properties
- 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.
Irregular Quotients of which this is a minimal cover
None.
Representations
Permutation Representation (GAP)
s0 := ( 71,106)( 72,107)( 73,108)( 74,109)( 75,110)( 76,111)( 77,112)( 78,113)( 79,114)( 80,115)( 81,116)( 82,117)( 83,118)( 84,119)( 85,120)( 86,121)( 87,122)( 88,123)( 89,124)( 90,125)( 91,126)( 92,127)( 93,128)( 94,129)( 95,130)( 96,131)( 97,132)( 98,133)( 99,134)(100,135)(101,136)(102,137)(103,138)(104,139)(105,140);; s1 := ( 1, 71)( 2, 72)( 3, 73)( 4, 74)( 5, 75)( 6, 76)( 7, 77)( 8, 99)( 9,100)( 10,101)( 11,102)( 12,103)( 13,104)( 14,105)( 15, 92)( 16, 93)( 17, 94)( 18, 95)( 19, 96)( 20, 97)( 21, 98)( 22, 85)( 23, 86)( 24, 87)( 25, 88)( 26, 89)( 27, 90)( 28, 91)( 29, 78)( 30, 79)( 31, 80)( 32, 81)( 33, 82)( 34, 83)( 35, 84)( 36,106)( 37,107)( 38,108)( 39,109)( 40,110)( 41,111)( 42,112)( 43,134)( 44,135)( 45,136)( 46,137)( 47,138)( 48,139)( 49,140)( 50,127)( 51,128)( 52,129)( 53,130)( 54,131)( 55,132)( 56,133)( 57,120)( 58,121)( 59,122)( 60,123)( 61,124)( 62,125)( 63,126)( 64,113)( 65,114)( 66,115)( 67,116)( 68,117)( 69,118)( 70,119);; s2 := ( 1, 8)( 2, 14)( 3, 13)( 4, 12)( 5, 11)( 6, 10)( 7, 9)( 15, 29)( 16, 35)( 17, 34)( 18, 33)( 19, 32)( 20, 31)( 21, 30)( 23, 28)( 24, 27)( 25, 26)( 36, 43)( 37, 49)( 38, 48)( 39, 47)( 40, 46)( 41, 45)( 42, 44)( 50, 64)( 51, 70)( 52, 69)( 53, 68)( 54, 67)( 55, 66)( 56, 65)( 58, 63)( 59, 62)( 60, 61)( 71, 78)( 72, 84)( 73, 83)( 74, 82)( 75, 81)( 76, 80)( 77, 79)( 85, 99)( 86,105)( 87,104)( 88,103)( 89,102)( 90,101)( 91,100)( 93, 98)( 94, 97)( 95, 96)(106,113)(107,119)(108,118)(109,117)(110,116)(111,115)(112,114)(120,134)(121,140)(122,139)(123,138)(124,137)(125,136)(126,135)(128,133)(129,132)(130,131);; s3 := ( 1, 2)( 3, 7)( 4, 6)( 8, 9)( 10, 14)( 11, 13)( 15, 16)( 17, 21)( 18, 20)( 22, 23)( 24, 28)( 25, 27)( 29, 30)( 31, 35)( 32, 34)( 36, 37)( 38, 42)( 39, 41)( 43, 44)( 45, 49)( 46, 48)( 50, 51)( 52, 56)( 53, 55)( 57, 58)( 59, 63)( 60, 62)( 64, 65)( 66, 70)( 67, 69)( 71, 72)( 73, 77)( 74, 76)( 78, 79)( 80, 84)( 81, 83)( 85, 86)( 87, 91)( 88, 90)( 92, 93)( 94, 98)( 95, 97)( 99,100)(101,105)(102,104)(106,107)(108,112)(109,111)(113,114)(115,119)(116,118)(120,121)(122,126)(123,125)(127,128)(129,133)(130,132)(134,135)(136,140)(137,139);; 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, s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s3*s2*s1*s2*s3*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(140)!( 71,106)( 72,107)( 73,108)( 74,109)( 75,110)( 76,111)( 77,112)( 78,113)( 79,114)( 80,115)( 81,116)( 82,117)( 83,118)( 84,119)( 85,120)( 86,121)( 87,122)( 88,123)( 89,124)( 90,125)( 91,126)( 92,127)( 93,128)( 94,129)( 95,130)( 96,131)( 97,132)( 98,133)( 99,134)(100,135)(101,136)(102,137)(103,138)(104,139)(105,140); s1 := Sym(140)!( 1, 71)( 2, 72)( 3, 73)( 4, 74)( 5, 75)( 6, 76)( 7, 77)( 8, 99)( 9,100)( 10,101)( 11,102)( 12,103)( 13,104)( 14,105)( 15, 92)( 16, 93)( 17, 94)( 18, 95)( 19, 96)( 20, 97)( 21, 98)( 22, 85)( 23, 86)( 24, 87)( 25, 88)( 26, 89)( 27, 90)( 28, 91)( 29, 78)( 30, 79)( 31, 80)( 32, 81)( 33, 82)( 34, 83)( 35, 84)( 36,106)( 37,107)( 38,108)( 39,109)( 40,110)( 41,111)( 42,112)( 43,134)( 44,135)( 45,136)( 46,137)( 47,138)( 48,139)( 49,140)( 50,127)( 51,128)( 52,129)( 53,130)( 54,131)( 55,132)( 56,133)( 57,120)( 58,121)( 59,122)( 60,123)( 61,124)( 62,125)( 63,126)( 64,113)( 65,114)( 66,115)( 67,116)( 68,117)( 69,118)( 70,119); s2 := Sym(140)!( 1, 8)( 2, 14)( 3, 13)( 4, 12)( 5, 11)( 6, 10)( 7, 9)( 15, 29)( 16, 35)( 17, 34)( 18, 33)( 19, 32)( 20, 31)( 21, 30)( 23, 28)( 24, 27)( 25, 26)( 36, 43)( 37, 49)( 38, 48)( 39, 47)( 40, 46)( 41, 45)( 42, 44)( 50, 64)( 51, 70)( 52, 69)( 53, 68)( 54, 67)( 55, 66)( 56, 65)( 58, 63)( 59, 62)( 60, 61)( 71, 78)( 72, 84)( 73, 83)( 74, 82)( 75, 81)( 76, 80)( 77, 79)( 85, 99)( 86,105)( 87,104)( 88,103)( 89,102)( 90,101)( 91,100)( 93, 98)( 94, 97)( 95, 96)(106,113)(107,119)(108,118)(109,117)(110,116)(111,115)(112,114)(120,134)(121,140)(122,139)(123,138)(124,137)(125,136)(126,135)(128,133)(129,132)(130,131); s3 := Sym(140)!( 1, 2)( 3, 7)( 4, 6)( 8, 9)( 10, 14)( 11, 13)( 15, 16)( 17, 21)( 18, 20)( 22, 23)( 24, 28)( 25, 27)( 29, 30)( 31, 35)( 32, 34)( 36, 37)( 38, 42)( 39, 41)( 43, 44)( 45, 49)( 46, 48)( 50, 51)( 52, 56)( 53, 55)( 57, 58)( 59, 63)( 60, 62)( 64, 65)( 66, 70)( 67, 69)( 71, 72)( 73, 77)( 74, 76)( 78, 79)( 80, 84)( 81, 83)( 85, 86)( 87, 91)( 88, 90)( 92, 93)( 94, 98)( 95, 97)( 99,100)(101,105)(102,104)(106,107)(108,112)(109,111)(113,114)(115,119)(116,118)(120,121)(122,126)(123,125)(127,128)(129,133)(130,132)(134,135)(136,140)(137,139); poly := sub<Sym(140)|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, s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s3*s2*s1*s2*s3*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;
References
None.
to this polytope.