Overview
- Group
- SmallGroup(1344,8483)
- Rank
- 4
- Schläfli Type
- {2,56,6}
- Vertices, edges, …
- 2, 56, 168, 6
- Order of s0s1s2s3
- 168
- Order of s0s1s2s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Degenerate
- 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.
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := ( 4, 9)( 5, 8)( 6, 7)( 11, 16)( 12, 15)( 13, 14)( 18, 23)( 19, 22)( 20, 21)( 25, 30)( 26, 29)( 27, 28)( 32, 37)( 33, 36)( 34, 35)( 39, 44)( 40, 43)( 41, 42)( 45, 66)( 46, 72)( 47, 71)( 48, 70)( 49, 69)( 50, 68)( 51, 67)( 52, 73)( 53, 79)( 54, 78)( 55, 77)( 56, 76)( 57, 75)( 58, 74)( 59, 80)( 60, 86)( 61, 85)( 62, 84)( 63, 83)( 64, 82)( 65, 81)( 87,129)( 88,135)( 89,134)( 90,133)( 91,132)( 92,131)( 93,130)( 94,136)( 95,142)( 96,141)( 97,140)( 98,139)( 99,138)(100,137)(101,143)(102,149)(103,148)(104,147)(105,146)(106,145)(107,144)(108,150)(109,156)(110,155)(111,154)(112,153)(113,152)(114,151)(115,157)(116,163)(117,162)(118,161)(119,160)(120,159)(121,158)(122,164)(123,170)(124,169)(125,168)(126,167)(127,166)(128,165);; s2 := ( 3, 88)( 4, 87)( 5, 93)( 6, 92)( 7, 91)( 8, 90)( 9, 89)( 10,102)( 11,101)( 12,107)( 13,106)( 14,105)( 15,104)( 16,103)( 17, 95)( 18, 94)( 19,100)( 20, 99)( 21, 98)( 22, 97)( 23, 96)( 24,109)( 25,108)( 26,114)( 27,113)( 28,112)( 29,111)( 30,110)( 31,123)( 32,122)( 33,128)( 34,127)( 35,126)( 36,125)( 37,124)( 38,116)( 39,115)( 40,121)( 41,120)( 42,119)( 43,118)( 44,117)( 45,151)( 46,150)( 47,156)( 48,155)( 49,154)( 50,153)( 51,152)( 52,165)( 53,164)( 54,170)( 55,169)( 56,168)( 57,167)( 58,166)( 59,158)( 60,157)( 61,163)( 62,162)( 63,161)( 64,160)( 65,159)( 66,130)( 67,129)( 68,135)( 69,134)( 70,133)( 71,132)( 72,131)( 73,144)( 74,143)( 75,149)( 76,148)( 77,147)( 78,146)( 79,145)( 80,137)( 81,136)( 82,142)( 83,141)( 84,140)( 85,139)( 86,138);; s3 := ( 3, 10)( 4, 11)( 5, 12)( 6, 13)( 7, 14)( 8, 15)( 9, 16)( 24, 31)( 25, 32)( 26, 33)( 27, 34)( 28, 35)( 29, 36)( 30, 37)( 45, 52)( 46, 53)( 47, 54)( 48, 55)( 49, 56)( 50, 57)( 51, 58)( 66, 73)( 67, 74)( 68, 75)( 69, 76)( 70, 77)( 71, 78)( 72, 79)( 87, 94)( 88, 95)( 89, 96)( 90, 97)( 91, 98)( 92, 99)( 93,100)(108,115)(109,116)(110,117)(111,118)(112,119)(113,120)(114,121)(129,136)(130,137)(131,138)(132,139)(133,140)(134,141)(135,142)(150,157)(151,158)(152,159)(153,160)(154,161)(155,162)(156,163);; 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*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
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*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(170)!(1,2); s1 := Sym(170)!( 4, 9)( 5, 8)( 6, 7)( 11, 16)( 12, 15)( 13, 14)( 18, 23)( 19, 22)( 20, 21)( 25, 30)( 26, 29)( 27, 28)( 32, 37)( 33, 36)( 34, 35)( 39, 44)( 40, 43)( 41, 42)( 45, 66)( 46, 72)( 47, 71)( 48, 70)( 49, 69)( 50, 68)( 51, 67)( 52, 73)( 53, 79)( 54, 78)( 55, 77)( 56, 76)( 57, 75)( 58, 74)( 59, 80)( 60, 86)( 61, 85)( 62, 84)( 63, 83)( 64, 82)( 65, 81)( 87,129)( 88,135)( 89,134)( 90,133)( 91,132)( 92,131)( 93,130)( 94,136)( 95,142)( 96,141)( 97,140)( 98,139)( 99,138)(100,137)(101,143)(102,149)(103,148)(104,147)(105,146)(106,145)(107,144)(108,150)(109,156)(110,155)(111,154)(112,153)(113,152)(114,151)(115,157)(116,163)(117,162)(118,161)(119,160)(120,159)(121,158)(122,164)(123,170)(124,169)(125,168)(126,167)(127,166)(128,165); s2 := Sym(170)!( 3, 88)( 4, 87)( 5, 93)( 6, 92)( 7, 91)( 8, 90)( 9, 89)( 10,102)( 11,101)( 12,107)( 13,106)( 14,105)( 15,104)( 16,103)( 17, 95)( 18, 94)( 19,100)( 20, 99)( 21, 98)( 22, 97)( 23, 96)( 24,109)( 25,108)( 26,114)( 27,113)( 28,112)( 29,111)( 30,110)( 31,123)( 32,122)( 33,128)( 34,127)( 35,126)( 36,125)( 37,124)( 38,116)( 39,115)( 40,121)( 41,120)( 42,119)( 43,118)( 44,117)( 45,151)( 46,150)( 47,156)( 48,155)( 49,154)( 50,153)( 51,152)( 52,165)( 53,164)( 54,170)( 55,169)( 56,168)( 57,167)( 58,166)( 59,158)( 60,157)( 61,163)( 62,162)( 63,161)( 64,160)( 65,159)( 66,130)( 67,129)( 68,135)( 69,134)( 70,133)( 71,132)( 72,131)( 73,144)( 74,143)( 75,149)( 76,148)( 77,147)( 78,146)( 79,145)( 80,137)( 81,136)( 82,142)( 83,141)( 84,140)( 85,139)( 86,138); s3 := Sym(170)!( 3, 10)( 4, 11)( 5, 12)( 6, 13)( 7, 14)( 8, 15)( 9, 16)( 24, 31)( 25, 32)( 26, 33)( 27, 34)( 28, 35)( 29, 36)( 30, 37)( 45, 52)( 46, 53)( 47, 54)( 48, 55)( 49, 56)( 50, 57)( 51, 58)( 66, 73)( 67, 74)( 68, 75)( 69, 76)( 70, 77)( 71, 78)( 72, 79)( 87, 94)( 88, 95)( 89, 96)( 90, 97)( 91, 98)( 92, 99)( 93,100)(108,115)(109,116)(110,117)(111,118)(112,119)(113,120)(114,121)(129,136)(130,137)(131,138)(132,139)(133,140)(134,141)(135,142)(150,157)(151,158)(152,159)(153,160)(154,161)(155,162)(156,163); poly := sub<Sym(170)|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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 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*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 >;