Overview
- Group
- SmallGroup(1344,8561)
- Rank
- 4
- Schläfli Type
- {14,6,8}
- Vertices, edges, …
- 14, 42, 24, 8
- Order of s0s1s2s3
- 168
- Order of s0s1s2s3s2s1
- 2
- Also known as
- {{14,6|2},{6,8|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
12-fold
14-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, 16)( 9, 15)( 10, 21)( 11, 20)( 12, 19)( 13, 18)( 14, 17)( 22, 23)( 24, 28)( 25, 27)( 29, 37)( 30, 36)( 31, 42)( 32, 41)( 33, 40)( 34, 39)( 35, 38)( 43, 44)( 45, 49)( 46, 48)( 50, 58)( 51, 57)( 52, 63)( 53, 62)( 54, 61)( 55, 60)( 56, 59)( 64, 65)( 66, 70)( 67, 69)( 71, 79)( 72, 78)( 73, 84)( 74, 83)( 75, 82)( 76, 81)( 77, 80)( 85, 86)( 87, 91)( 88, 90)( 92,100)( 93, 99)( 94,105)( 95,104)( 96,103)( 97,102)( 98,101)(106,107)(108,112)(109,111)(113,121)(114,120)(115,126)(116,125)(117,124)(118,123)(119,122)(127,128)(129,133)(130,132)(134,142)(135,141)(136,147)(137,146)(138,145)(139,144)(140,143)(148,149)(150,154)(151,153)(155,163)(156,162)(157,168)(158,167)(159,166)(160,165)(161,164);; 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, 71)( 44, 72)( 45, 73)( 46, 74)( 47, 75)( 48, 76)( 49, 77)( 50, 64)( 51, 65)( 52, 66)( 53, 67)( 54, 68)( 55, 69)( 56, 70)( 57, 78)( 58, 79)( 59, 80)( 60, 81)( 61, 82)( 62, 83)( 63, 84)( 85,134)( 86,135)( 87,136)( 88,137)( 89,138)( 90,139)( 91,140)( 92,127)( 93,128)( 94,129)( 95,130)( 96,131)( 97,132)( 98,133)( 99,141)(100,142)(101,143)(102,144)(103,145)(104,146)(105,147)(106,155)(107,156)(108,157)(109,158)(110,159)(111,160)(112,161)(113,148)(114,149)(115,150)(116,151)(117,152)(118,153)(119,154)(120,162)(121,163)(122,164)(123,165)(124,166)(125,167)(126,168);; s3 := ( 1, 85)( 2, 86)( 3, 87)( 4, 88)( 5, 89)( 6, 90)( 7, 91)( 8, 92)( 9, 93)( 10, 94)( 11, 95)( 12, 96)( 13, 97)( 14, 98)( 15, 99)( 16,100)( 17,101)( 18,102)( 19,103)( 20,104)( 21,105)( 22,106)( 23,107)( 24,108)( 25,109)( 26,110)( 27,111)( 28,112)( 29,113)( 30,114)( 31,115)( 32,116)( 33,117)( 34,118)( 35,119)( 36,120)( 37,121)( 38,122)( 39,123)( 40,124)( 41,125)( 42,126)( 43,148)( 44,149)( 45,150)( 46,151)( 47,152)( 48,153)( 49,154)( 50,155)( 51,156)( 52,157)( 53,158)( 54,159)( 55,160)( 56,161)( 57,162)( 58,163)( 59,164)( 60,165)( 61,166)( 62,167)( 63,168)( 64,127)( 65,128)( 66,129)( 67,130)( 68,131)( 69,132)( 70,133)( 71,134)( 72,135)( 73,136)( 74,137)( 75,138)( 76,139)( 77,140)( 78,141)( 79,142)( 80,143)( 81,144)( 82,145)( 83,146)( 84,147);; 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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
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, 16)( 9, 15)( 10, 21)( 11, 20)( 12, 19)( 13, 18)( 14, 17)( 22, 23)( 24, 28)( 25, 27)( 29, 37)( 30, 36)( 31, 42)( 32, 41)( 33, 40)( 34, 39)( 35, 38)( 43, 44)( 45, 49)( 46, 48)( 50, 58)( 51, 57)( 52, 63)( 53, 62)( 54, 61)( 55, 60)( 56, 59)( 64, 65)( 66, 70)( 67, 69)( 71, 79)( 72, 78)( 73, 84)( 74, 83)( 75, 82)( 76, 81)( 77, 80)( 85, 86)( 87, 91)( 88, 90)( 92,100)( 93, 99)( 94,105)( 95,104)( 96,103)( 97,102)( 98,101)(106,107)(108,112)(109,111)(113,121)(114,120)(115,126)(116,125)(117,124)(118,123)(119,122)(127,128)(129,133)(130,132)(134,142)(135,141)(136,147)(137,146)(138,145)(139,144)(140,143)(148,149)(150,154)(151,153)(155,163)(156,162)(157,168)(158,167)(159,166)(160,165)(161,164); 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, 71)( 44, 72)( 45, 73)( 46, 74)( 47, 75)( 48, 76)( 49, 77)( 50, 64)( 51, 65)( 52, 66)( 53, 67)( 54, 68)( 55, 69)( 56, 70)( 57, 78)( 58, 79)( 59, 80)( 60, 81)( 61, 82)( 62, 83)( 63, 84)( 85,134)( 86,135)( 87,136)( 88,137)( 89,138)( 90,139)( 91,140)( 92,127)( 93,128)( 94,129)( 95,130)( 96,131)( 97,132)( 98,133)( 99,141)(100,142)(101,143)(102,144)(103,145)(104,146)(105,147)(106,155)(107,156)(108,157)(109,158)(110,159)(111,160)(112,161)(113,148)(114,149)(115,150)(116,151)(117,152)(118,153)(119,154)(120,162)(121,163)(122,164)(123,165)(124,166)(125,167)(126,168); s3 := Sym(168)!( 1, 85)( 2, 86)( 3, 87)( 4, 88)( 5, 89)( 6, 90)( 7, 91)( 8, 92)( 9, 93)( 10, 94)( 11, 95)( 12, 96)( 13, 97)( 14, 98)( 15, 99)( 16,100)( 17,101)( 18,102)( 19,103)( 20,104)( 21,105)( 22,106)( 23,107)( 24,108)( 25,109)( 26,110)( 27,111)( 28,112)( 29,113)( 30,114)( 31,115)( 32,116)( 33,117)( 34,118)( 35,119)( 36,120)( 37,121)( 38,122)( 39,123)( 40,124)( 41,125)( 42,126)( 43,148)( 44,149)( 45,150)( 46,151)( 47,152)( 48,153)( 49,154)( 50,155)( 51,156)( 52,157)( 53,158)( 54,159)( 55,160)( 56,161)( 57,162)( 58,163)( 59,164)( 60,165)( 61,166)( 62,167)( 63,168)( 64,127)( 65,128)( 66,129)( 67,130)( 68,131)( 69,132)( 70,133)( 71,134)( 72,135)( 73,136)( 74,137)( 75,138)( 76,139)( 77,140)( 78,141)( 79,142)( 80,143)( 81,144)( 82,145)( 83,146)( 84,147); 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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 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.