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