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