Overview
- Group
- SmallGroup(672,392)
- Rank
- 3
- Schläfli Type
- {14,24}
- Vertices, edges, …
- 14, 168, 24
- Order of s0s1s2
- 168
- Order of s0s1s2s1
- 2
- Also known as
- {14,24|2}. if this polytope has another name.
Special Properties
- Compact Hyperbolic Quotient
- Locally Spherical
- Orientable
- Flat
Quotients maximal quotients in bold
2-fold
3-fold
4-fold
6-fold
7-fold
12-fold
14-fold
21-fold
24-fold
28-fold
42-fold
56-fold
84-fold
Covers minimal covers in bold
2-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)(142,147)(143,146)(144,145)(149,154)(150,153)(151,152)(156,161)(157,160)(158,159)(163,168)(164,167)(165,166);; s1 := ( 1, 2)( 3, 7)( 4, 6)( 8, 16)( 9, 15)( 10, 21)( 11, 20)( 12, 19)( 13, 18)( 14, 17)( 22, 23)( 24, 28)( 25, 27)( 29, 37)( 30, 36)( 31, 42)( 32, 41)( 33, 40)( 34, 39)( 35, 38)( 43, 65)( 44, 64)( 45, 70)( 46, 69)( 47, 68)( 48, 67)( 49, 66)( 50, 79)( 51, 78)( 52, 84)( 53, 83)( 54, 82)( 55, 81)( 56, 80)( 57, 72)( 58, 71)( 59, 77)( 60, 76)( 61, 75)( 62, 74)( 63, 73)( 85,128)( 86,127)( 87,133)( 88,132)( 89,131)( 90,130)( 91,129)( 92,142)( 93,141)( 94,147)( 95,146)( 96,145)( 97,144)( 98,143)( 99,135)(100,134)(101,140)(102,139)(103,138)(104,137)(105,136)(106,149)(107,148)(108,154)(109,153)(110,152)(111,151)(112,150)(113,163)(114,162)(115,168)(116,167)(117,166)(118,165)(119,164)(120,156)(121,155)(122,161)(123,160)(124,159)(125,158)(126,157);; s2 := ( 1, 92)( 2, 93)( 3, 94)( 4, 95)( 5, 96)( 6, 97)( 7, 98)( 8, 85)( 9, 86)( 10, 87)( 11, 88)( 12, 89)( 13, 90)( 14, 91)( 15, 99)( 16,100)( 17,101)( 18,102)( 19,103)( 20,104)( 21,105)( 22,113)( 23,114)( 24,115)( 25,116)( 26,117)( 27,118)( 28,119)( 29,106)( 30,107)( 31,108)( 32,109)( 33,110)( 34,111)( 35,112)( 36,120)( 37,121)( 38,122)( 39,123)( 40,124)( 41,125)( 42,126)( 43,155)( 44,156)( 45,157)( 46,158)( 47,159)( 48,160)( 49,161)( 50,148)( 51,149)( 52,150)( 53,151)( 54,152)( 55,153)( 56,154)( 57,162)( 58,163)( 59,164)( 60,165)( 61,166)( 62,167)( 63,168)( 64,134)( 65,135)( 66,136)( 67,137)( 68,138)( 69,139)( 70,140)( 71,127)( 72,128)( 73,129)( 74,130)( 75,131)( 76,132)( 77,133)( 78,141)( 79,142)( 80,143)( 81,144)( 82,145)( 83,146)( 84,147);; 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*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(168)!( 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)(142,147)(143,146)(144,145)(149,154)(150,153)(151,152)(156,161)(157,160)(158,159)(163,168)(164,167)(165,166); s1 := Sym(168)!( 1, 2)( 3, 7)( 4, 6)( 8, 16)( 9, 15)( 10, 21)( 11, 20)( 12, 19)( 13, 18)( 14, 17)( 22, 23)( 24, 28)( 25, 27)( 29, 37)( 30, 36)( 31, 42)( 32, 41)( 33, 40)( 34, 39)( 35, 38)( 43, 65)( 44, 64)( 45, 70)( 46, 69)( 47, 68)( 48, 67)( 49, 66)( 50, 79)( 51, 78)( 52, 84)( 53, 83)( 54, 82)( 55, 81)( 56, 80)( 57, 72)( 58, 71)( 59, 77)( 60, 76)( 61, 75)( 62, 74)( 63, 73)( 85,128)( 86,127)( 87,133)( 88,132)( 89,131)( 90,130)( 91,129)( 92,142)( 93,141)( 94,147)( 95,146)( 96,145)( 97,144)( 98,143)( 99,135)(100,134)(101,140)(102,139)(103,138)(104,137)(105,136)(106,149)(107,148)(108,154)(109,153)(110,152)(111,151)(112,150)(113,163)(114,162)(115,168)(116,167)(117,166)(118,165)(119,164)(120,156)(121,155)(122,161)(123,160)(124,159)(125,158)(126,157); s2 := Sym(168)!( 1, 92)( 2, 93)( 3, 94)( 4, 95)( 5, 96)( 6, 97)( 7, 98)( 8, 85)( 9, 86)( 10, 87)( 11, 88)( 12, 89)( 13, 90)( 14, 91)( 15, 99)( 16,100)( 17,101)( 18,102)( 19,103)( 20,104)( 21,105)( 22,113)( 23,114)( 24,115)( 25,116)( 26,117)( 27,118)( 28,119)( 29,106)( 30,107)( 31,108)( 32,109)( 33,110)( 34,111)( 35,112)( 36,120)( 37,121)( 38,122)( 39,123)( 40,124)( 41,125)( 42,126)( 43,155)( 44,156)( 45,157)( 46,158)( 47,159)( 48,160)( 49,161)( 50,148)( 51,149)( 52,150)( 53,151)( 54,152)( 55,153)( 56,154)( 57,162)( 58,163)( 59,164)( 60,165)( 61,166)( 62,167)( 63,168)( 64,134)( 65,135)( 66,136)( 67,137)( 68,138)( 69,139)( 70,140)( 71,127)( 72,128)( 73,129)( 74,130)( 75,131)( 76,132)( 77,133)( 78,141)( 79,142)( 80,143)( 81,144)( 82,145)( 83,146)( 84,147); poly := sub<Sym(168)|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*s1*s2*s1*s2*s1*s2*s1*s2 >;
References
None.
to this polytope.