Overview
- Group
- SmallGroup(560,120)
- Rank
- 3
- Schläfli Type
- {14,20}
- Vertices, edges, …
- 14, 140, 20
- Order of s0s1s2
- 140
- Order of s0s1s2s1
- 2
- Also known as
- {14,20|2}. if this polytope has another name.
Special Properties
- Compact Hyperbolic Quotient
- Locally Spherical
- 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
2-fold
3-fold
Irregular Quotients of which this is a minimal cover
None.
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)( 72, 77)( 73, 76)( 74, 75)( 79, 84)( 80, 83)( 81, 82)( 86, 91)( 87, 90)( 88, 89)( 93, 98)( 94, 97)( 95, 96)(100,105)(101,104)(102,103)(107,112)(108,111)(109,110)(114,119)(115,118)(116,117)(121,126)(122,125)(123,124)(128,133)(129,132)(130,131)(135,140)(136,139)(137,138);; s1 := ( 1, 2)( 3, 7)( 4, 6)( 8, 30)( 9, 29)( 10, 35)( 11, 34)( 12, 33)( 13, 32)( 14, 31)( 15, 23)( 16, 22)( 17, 28)( 18, 27)( 19, 26)( 20, 25)( 21, 24)( 36, 37)( 38, 42)( 39, 41)( 43, 65)( 44, 64)( 45, 70)( 46, 69)( 47, 68)( 48, 67)( 49, 66)( 50, 58)( 51, 57)( 52, 63)( 53, 62)( 54, 61)( 55, 60)( 56, 59)( 71,107)( 72,106)( 73,112)( 74,111)( 75,110)( 76,109)( 77,108)( 78,135)( 79,134)( 80,140)( 81,139)( 82,138)( 83,137)( 84,136)( 85,128)( 86,127)( 87,133)( 88,132)( 89,131)( 90,130)( 91,129)( 92,121)( 93,120)( 94,126)( 95,125)( 96,124)( 97,123)( 98,122)( 99,114)(100,113)(101,119)(102,118)(103,117)(104,116)(105,115);; s2 := ( 1, 78)( 2, 79)( 3, 80)( 4, 81)( 5, 82)( 6, 83)( 7, 84)( 8, 71)( 9, 72)( 10, 73)( 11, 74)( 12, 75)( 13, 76)( 14, 77)( 15, 99)( 16,100)( 17,101)( 18,102)( 19,103)( 20,104)( 21,105)( 22, 92)( 23, 93)( 24, 94)( 25, 95)( 26, 96)( 27, 97)( 28, 98)( 29, 85)( 30, 86)( 31, 87)( 32, 88)( 33, 89)( 34, 90)( 35, 91)( 36,113)( 37,114)( 38,115)( 39,116)( 40,117)( 41,118)( 42,119)( 43,106)( 44,107)( 45,108)( 46,109)( 47,110)( 48,111)( 49,112)( 50,134)( 51,135)( 52,136)( 53,137)( 54,138)( 55,139)( 56,140)( 57,127)( 58,128)( 59,129)( 60,130)( 61,131)( 62,132)( 63,133)( 64,120)( 65,121)( 66,122)( 67,123)( 68,124)( 69,125)( 70,126);; poly := Group([s0,s1,s2]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1","s2");;
s0 := F.1;; s1 := F.2;; s2 := F.3;;
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s2*s1*s0*s1*s2*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,
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(140)!( 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)( 72, 77)( 73, 76)( 74, 75)( 79, 84)( 80, 83)( 81, 82)( 86, 91)( 87, 90)( 88, 89)( 93, 98)( 94, 97)( 95, 96)(100,105)(101,104)(102,103)(107,112)(108,111)(109,110)(114,119)(115,118)(116,117)(121,126)(122,125)(123,124)(128,133)(129,132)(130,131)(135,140)(136,139)(137,138); s1 := Sym(140)!( 1, 2)( 3, 7)( 4, 6)( 8, 30)( 9, 29)( 10, 35)( 11, 34)( 12, 33)( 13, 32)( 14, 31)( 15, 23)( 16, 22)( 17, 28)( 18, 27)( 19, 26)( 20, 25)( 21, 24)( 36, 37)( 38, 42)( 39, 41)( 43, 65)( 44, 64)( 45, 70)( 46, 69)( 47, 68)( 48, 67)( 49, 66)( 50, 58)( 51, 57)( 52, 63)( 53, 62)( 54, 61)( 55, 60)( 56, 59)( 71,107)( 72,106)( 73,112)( 74,111)( 75,110)( 76,109)( 77,108)( 78,135)( 79,134)( 80,140)( 81,139)( 82,138)( 83,137)( 84,136)( 85,128)( 86,127)( 87,133)( 88,132)( 89,131)( 90,130)( 91,129)( 92,121)( 93,120)( 94,126)( 95,125)( 96,124)( 97,123)( 98,122)( 99,114)(100,113)(101,119)(102,118)(103,117)(104,116)(105,115); s2 := Sym(140)!( 1, 78)( 2, 79)( 3, 80)( 4, 81)( 5, 82)( 6, 83)( 7, 84)( 8, 71)( 9, 72)( 10, 73)( 11, 74)( 12, 75)( 13, 76)( 14, 77)( 15, 99)( 16,100)( 17,101)( 18,102)( 19,103)( 20,104)( 21,105)( 22, 92)( 23, 93)( 24, 94)( 25, 95)( 26, 96)( 27, 97)( 28, 98)( 29, 85)( 30, 86)( 31, 87)( 32, 88)( 33, 89)( 34, 90)( 35, 91)( 36,113)( 37,114)( 38,115)( 39,116)( 40,117)( 41,118)( 42,119)( 43,106)( 44,107)( 45,108)( 46,109)( 47,110)( 48,111)( 49,112)( 50,134)( 51,135)( 52,136)( 53,137)( 54,138)( 55,139)( 56,140)( 57,127)( 58,128)( 59,129)( 60,130)( 61,131)( 62,132)( 63,133)( 64,120)( 65,121)( 66,122)( 67,123)( 68,124)( 69,125)( 70,126); poly := sub<Sym(140)|s0,s1,s2>;
Finitely Presented Group Representation (Magma)
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s2*s1*s0*s1*s2*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, 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 >;
References
None.
to this polytope.