Overview
- Group
- SmallGroup(1344,8561)
- Rank
- 4
- Schläfli Type
- {14,8,6}
- Vertices, edges, …
- 14, 56, 24, 6
- Order of s0s1s2s3
- 168
- Order of s0s1s2s3s2s1
- 2
- Also known as
- {{14,8|2},{8,6|2}}. if this polytope has another name.
Special Properties
- Universal
- Orientable
- Flat
Quotients maximal quotients in bold
2-fold
3-fold
4-fold
6-fold
7-fold
8-fold
12-fold
14-fold
16-fold
21-fold
24-fold
28-fold
42-fold
56-fold
84-fold
Covers minimal covers in bold
None in this atlas.
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, 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, 65)( 44, 64)( 45, 70)( 46, 69)( 47, 68)( 48, 67)( 49, 66)( 50, 72)( 51, 71)( 52, 77)( 53, 76)( 54, 75)( 55, 74)( 56, 73)( 57, 79)( 58, 78)( 59, 84)( 60, 83)( 61, 82)( 62, 81)( 63, 80)( 85,128)( 86,127)( 87,133)( 88,132)( 89,131)( 90,130)( 91,129)( 92,135)( 93,134)( 94,140)( 95,139)( 96,138)( 97,137)( 98,136)( 99,142)(100,141)(101,147)(102,146)(103,145)(104,144)(105,143)(106,149)(107,148)(108,154)(109,153)(110,152)(111,151)(112,150)(113,156)(114,155)(115,161)(116,160)(117,159)(118,158)(119,157)(120,163)(121,162)(122,168)(123,167)(124,166)(125,165)(126,164);; s2 := ( 1, 85)( 2, 86)( 3, 87)( 4, 88)( 5, 89)( 6, 90)( 7, 91)( 8, 99)( 9,100)( 10,101)( 11,102)( 12,103)( 13,104)( 14,105)( 15, 92)( 16, 93)( 17, 94)( 18, 95)( 19, 96)( 20, 97)( 21, 98)( 22,106)( 23,107)( 24,108)( 25,109)( 26,110)( 27,111)( 28,112)( 29,120)( 30,121)( 31,122)( 32,123)( 33,124)( 34,125)( 35,126)( 36,113)( 37,114)( 38,115)( 39,116)( 40,117)( 41,118)( 42,119)( 43,148)( 44,149)( 45,150)( 46,151)( 47,152)( 48,153)( 49,154)( 50,162)( 51,163)( 52,164)( 53,165)( 54,166)( 55,167)( 56,168)( 57,155)( 58,156)( 59,157)( 60,158)( 61,159)( 62,160)( 63,161)( 64,127)( 65,128)( 66,129)( 67,130)( 68,131)( 69,132)( 70,133)( 71,141)( 72,142)( 73,143)( 74,144)( 75,145)( 76,146)( 77,147)( 78,134)( 79,135)( 80,136)( 81,137)( 82,138)( 83,139)( 84,140);; s3 := ( 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,s3]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s1*s2*s1*s0*s1*s2*s1,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
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 ];;
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, 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, 65)( 44, 64)( 45, 70)( 46, 69)( 47, 68)( 48, 67)( 49, 66)( 50, 72)( 51, 71)( 52, 77)( 53, 76)( 54, 75)( 55, 74)( 56, 73)( 57, 79)( 58, 78)( 59, 84)( 60, 83)( 61, 82)( 62, 81)( 63, 80)( 85,128)( 86,127)( 87,133)( 88,132)( 89,131)( 90,130)( 91,129)( 92,135)( 93,134)( 94,140)( 95,139)( 96,138)( 97,137)( 98,136)( 99,142)(100,141)(101,147)(102,146)(103,145)(104,144)(105,143)(106,149)(107,148)(108,154)(109,153)(110,152)(111,151)(112,150)(113,156)(114,155)(115,161)(116,160)(117,159)(118,158)(119,157)(120,163)(121,162)(122,168)(123,167)(124,166)(125,165)(126,164); s2 := Sym(168)!( 1, 85)( 2, 86)( 3, 87)( 4, 88)( 5, 89)( 6, 90)( 7, 91)( 8, 99)( 9,100)( 10,101)( 11,102)( 12,103)( 13,104)( 14,105)( 15, 92)( 16, 93)( 17, 94)( 18, 95)( 19, 96)( 20, 97)( 21, 98)( 22,106)( 23,107)( 24,108)( 25,109)( 26,110)( 27,111)( 28,112)( 29,120)( 30,121)( 31,122)( 32,123)( 33,124)( 34,125)( 35,126)( 36,113)( 37,114)( 38,115)( 39,116)( 40,117)( 41,118)( 42,119)( 43,148)( 44,149)( 45,150)( 46,151)( 47,152)( 48,153)( 49,154)( 50,162)( 51,163)( 52,164)( 53,165)( 54,166)( 55,167)( 56,168)( 57,155)( 58,156)( 59,157)( 60,158)( 61,159)( 62,160)( 63,161)( 64,127)( 65,128)( 66,129)( 67,130)( 68,131)( 69,132)( 70,133)( 71,141)( 72,142)( 73,143)( 74,144)( 75,145)( 76,146)( 77,147)( 78,134)( 79,135)( 80,136)( 81,137)( 82,138)( 83,139)( 84,140); s3 := 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,s3>;
Finitely Presented Group Representation (Magma)
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 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 >;
References
None.
to this polytope.