Overview
- Group
- SmallGroup(672,620)
- Rank
- 3
- Schläfli Type
- {28,12}
- Vertices, edges, …
- 28, 168, 12
- Order of s0s1s2
- 84
- Order of s0s1s2s1
- 2
- Also known as
- {28,12|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)( 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)( 43,128)( 44,127)( 45,133)( 46,132)( 47,131)( 48,130)( 49,129)( 50,142)( 51,141)( 52,147)( 53,146)( 54,145)( 55,144)( 56,143)( 57,135)( 58,134)( 59,140)( 60,139)( 61,138)( 62,137)( 63,136)( 64,149)( 65,148)( 66,154)( 67,153)( 68,152)( 69,151)( 70,150)( 71,163)( 72,162)( 73,168)( 74,167)( 75,166)( 76,165)( 77,164)( 78,156)( 79,155)( 80,161)( 81,160)( 82,159)( 83,158)( 84,157);; 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)( 85,113)( 86,114)( 87,115)( 88,116)( 89,117)( 90,118)( 91,119)( 92,106)( 93,107)( 94,108)( 95,109)( 96,110)( 97,111)( 98,112)( 99,120)(100,121)(101,122)(102,123)(103,124)(104,125)(105,126)(127,155)(128,156)(129,157)(130,158)(131,159)(132,160)(133,161)(134,148)(135,149)(136,150)(137,151)(138,152)(139,153)(140,154)(141,162)(142,163)(143,164)(144,165)(145,166)(146,167)(147,168);; 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,
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)( 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)( 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)( 43,128)( 44,127)( 45,133)( 46,132)( 47,131)( 48,130)( 49,129)( 50,142)( 51,141)( 52,147)( 53,146)( 54,145)( 55,144)( 56,143)( 57,135)( 58,134)( 59,140)( 60,139)( 61,138)( 62,137)( 63,136)( 64,149)( 65,148)( 66,154)( 67,153)( 68,152)( 69,151)( 70,150)( 71,163)( 72,162)( 73,168)( 74,167)( 75,166)( 76,165)( 77,164)( 78,156)( 79,155)( 80,161)( 81,160)( 82,159)( 83,158)( 84,157); 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)( 85,113)( 86,114)( 87,115)( 88,116)( 89,117)( 90,118)( 91,119)( 92,106)( 93,107)( 94,108)( 95,109)( 96,110)( 97,111)( 98,112)( 99,120)(100,121)(101,122)(102,123)(103,124)(104,125)(105,126)(127,155)(128,156)(129,157)(130,158)(131,159)(132,160)(133,161)(134,148)(135,149)(136,150)(137,151)(138,152)(139,153)(140,154)(141,162)(142,163)(143,164)(144,165)(145,166)(146,167)(147,168); 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, 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.