Overview
- Group
- SmallGroup(672,396)
- Rank
- 3
- Schläfli Type
- {56,6}
- Vertices, edges, …
- 56, 168, 6
- Order of s0s1s2
- 168
- Order of s0s1s2s1
- 2
- Also known as
- {56,6|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)( 43, 64)( 44, 70)( 45, 69)( 46, 68)( 47, 67)( 48, 66)( 49, 65)( 50, 71)( 51, 77)( 52, 76)( 53, 75)( 54, 74)( 55, 73)( 56, 72)( 57, 78)( 58, 84)( 59, 83)( 60, 82)( 61, 81)( 62, 80)( 63, 79)( 85,127)( 86,133)( 87,132)( 88,131)( 89,130)( 90,129)( 91,128)( 92,134)( 93,140)( 94,139)( 95,138)( 96,137)( 97,136)( 98,135)( 99,141)(100,147)(101,146)(102,145)(103,144)(104,143)(105,142)(106,148)(107,154)(108,153)(109,152)(110,151)(111,150)(112,149)(113,155)(114,161)(115,160)(116,159)(117,158)(118,157)(119,156)(120,162)(121,168)(122,167)(123,166)(124,165)(125,164)(126,163);; s1 := ( 1, 86)( 2, 85)( 3, 91)( 4, 90)( 5, 89)( 6, 88)( 7, 87)( 8,100)( 9, 99)( 10,105)( 11,104)( 12,103)( 13,102)( 14,101)( 15, 93)( 16, 92)( 17, 98)( 18, 97)( 19, 96)( 20, 95)( 21, 94)( 22,107)( 23,106)( 24,112)( 25,111)( 26,110)( 27,109)( 28,108)( 29,121)( 30,120)( 31,126)( 32,125)( 33,124)( 34,123)( 35,122)( 36,114)( 37,113)( 38,119)( 39,118)( 40,117)( 41,116)( 42,115)( 43,149)( 44,148)( 45,154)( 46,153)( 47,152)( 48,151)( 49,150)( 50,163)( 51,162)( 52,168)( 53,167)( 54,166)( 55,165)( 56,164)( 57,156)( 58,155)( 59,161)( 60,160)( 61,159)( 62,158)( 63,157)( 64,128)( 65,127)( 66,133)( 67,132)( 68,131)( 69,130)( 70,129)( 71,142)( 72,141)( 73,147)( 74,146)( 75,145)( 76,144)( 77,143)( 78,135)( 79,134)( 80,140)( 81,139)( 82,138)( 83,137)( 84,136);; s2 := ( 1, 8)( 2, 9)( 3, 10)( 4, 11)( 5, 12)( 6, 13)( 7, 14)( 22, 29)( 23, 30)( 24, 31)( 25, 32)( 26, 33)( 27, 34)( 28, 35)( 43, 50)( 44, 51)( 45, 52)( 46, 53)( 47, 54)( 48, 55)( 49, 56)( 64, 71)( 65, 72)( 66, 73)( 67, 74)( 68, 75)( 69, 76)( 70, 77)( 85, 92)( 86, 93)( 87, 94)( 88, 95)( 89, 96)( 90, 97)( 91, 98)(106,113)(107,114)(108,115)(109,116)(110,117)(111,118)(112,119)(127,134)(128,135)(129,136)(130,137)(131,138)(132,139)(133,140)(148,155)(149,156)(150,157)(151,158)(152,159)(153,160)(154,161);; 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,
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(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)( 43, 64)( 44, 70)( 45, 69)( 46, 68)( 47, 67)( 48, 66)( 49, 65)( 50, 71)( 51, 77)( 52, 76)( 53, 75)( 54, 74)( 55, 73)( 56, 72)( 57, 78)( 58, 84)( 59, 83)( 60, 82)( 61, 81)( 62, 80)( 63, 79)( 85,127)( 86,133)( 87,132)( 88,131)( 89,130)( 90,129)( 91,128)( 92,134)( 93,140)( 94,139)( 95,138)( 96,137)( 97,136)( 98,135)( 99,141)(100,147)(101,146)(102,145)(103,144)(104,143)(105,142)(106,148)(107,154)(108,153)(109,152)(110,151)(111,150)(112,149)(113,155)(114,161)(115,160)(116,159)(117,158)(118,157)(119,156)(120,162)(121,168)(122,167)(123,166)(124,165)(125,164)(126,163); s1 := Sym(168)!( 1, 86)( 2, 85)( 3, 91)( 4, 90)( 5, 89)( 6, 88)( 7, 87)( 8,100)( 9, 99)( 10,105)( 11,104)( 12,103)( 13,102)( 14,101)( 15, 93)( 16, 92)( 17, 98)( 18, 97)( 19, 96)( 20, 95)( 21, 94)( 22,107)( 23,106)( 24,112)( 25,111)( 26,110)( 27,109)( 28,108)( 29,121)( 30,120)( 31,126)( 32,125)( 33,124)( 34,123)( 35,122)( 36,114)( 37,113)( 38,119)( 39,118)( 40,117)( 41,116)( 42,115)( 43,149)( 44,148)( 45,154)( 46,153)( 47,152)( 48,151)( 49,150)( 50,163)( 51,162)( 52,168)( 53,167)( 54,166)( 55,165)( 56,164)( 57,156)( 58,155)( 59,161)( 60,160)( 61,159)( 62,158)( 63,157)( 64,128)( 65,127)( 66,133)( 67,132)( 68,131)( 69,130)( 70,129)( 71,142)( 72,141)( 73,147)( 74,146)( 75,145)( 76,144)( 77,143)( 78,135)( 79,134)( 80,140)( 81,139)( 82,138)( 83,137)( 84,136); s2 := Sym(168)!( 1, 8)( 2, 9)( 3, 10)( 4, 11)( 5, 12)( 6, 13)( 7, 14)( 22, 29)( 23, 30)( 24, 31)( 25, 32)( 26, 33)( 27, 34)( 28, 35)( 43, 50)( 44, 51)( 45, 52)( 46, 53)( 47, 54)( 48, 55)( 49, 56)( 64, 71)( 65, 72)( 66, 73)( 67, 74)( 68, 75)( 69, 76)( 70, 77)( 85, 92)( 86, 93)( 87, 94)( 88, 95)( 89, 96)( 90, 97)( 91, 98)(106,113)(107,114)(108,115)(109,116)(110,117)(111,118)(112,119)(127,134)(128,135)(129,136)(130,137)(131,138)(132,139)(133,140)(148,155)(149,156)(150,157)(151,158)(152,159)(153,160)(154,161); 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, 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 >;
References
None.
to this polytope.