Overview
- Group
- SmallGroup(1344,9160)
- Rank
- 4
- Schläfli Type
- {2,28,12}
- Vertices, edges, …
- 2, 28, 168, 12
- Order of s0s1s2s3
- 84
- 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)( 46, 51)( 47, 50)( 48, 49)( 53, 58)( 54, 57)( 55, 56)( 60, 65)( 61, 64)( 62, 63)( 67, 72)( 68, 71)( 69, 70)( 74, 79)( 75, 78)( 76, 77)( 81, 86)( 82, 85)( 83, 84)( 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)( 45,130)( 46,129)( 47,135)( 48,134)( 49,133)( 50,132)( 51,131)( 52,144)( 53,143)( 54,149)( 55,148)( 56,147)( 57,146)( 58,145)( 59,137)( 60,136)( 61,142)( 62,141)( 63,140)( 64,139)( 65,138)( 66,151)( 67,150)( 68,156)( 69,155)( 70,154)( 71,153)( 72,152)( 73,165)( 74,164)( 75,170)( 76,169)( 77,168)( 78,167)( 79,166)( 80,158)( 81,157)( 82,163)( 83,162)( 84,161)( 85,160)( 86,159);; 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)( 87,115)( 88,116)( 89,117)( 90,118)( 91,119)( 92,120)( 93,121)( 94,108)( 95,109)( 96,110)( 97,111)( 98,112)( 99,113)(100,114)(101,122)(102,123)(103,124)(104,125)(105,126)(106,127)(107,128)(129,157)(130,158)(131,159)(132,160)(133,161)(134,162)(135,163)(136,150)(137,151)(138,152)(139,153)(140,154)(141,155)(142,156)(143,164)(144,165)(145,166)(146,167)(147,168)(148,169)(149,170);; 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*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 ];;
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)( 46, 51)( 47, 50)( 48, 49)( 53, 58)( 54, 57)( 55, 56)( 60, 65)( 61, 64)( 62, 63)( 67, 72)( 68, 71)( 69, 70)( 74, 79)( 75, 78)( 76, 77)( 81, 86)( 82, 85)( 83, 84)( 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)( 45,130)( 46,129)( 47,135)( 48,134)( 49,133)( 50,132)( 51,131)( 52,144)( 53,143)( 54,149)( 55,148)( 56,147)( 57,146)( 58,145)( 59,137)( 60,136)( 61,142)( 62,141)( 63,140)( 64,139)( 65,138)( 66,151)( 67,150)( 68,156)( 69,155)( 70,154)( 71,153)( 72,152)( 73,165)( 74,164)( 75,170)( 76,169)( 77,168)( 78,167)( 79,166)( 80,158)( 81,157)( 82,163)( 83,162)( 84,161)( 85,160)( 86,159); 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)( 87,115)( 88,116)( 89,117)( 90,118)( 91,119)( 92,120)( 93,121)( 94,108)( 95,109)( 96,110)( 97,111)( 98,112)( 99,113)(100,114)(101,122)(102,123)(103,124)(104,125)(105,126)(106,127)(107,128)(129,157)(130,158)(131,159)(132,160)(133,161)(134,162)(135,163)(136,150)(137,151)(138,152)(139,153)(140,154)(141,155)(142,156)(143,164)(144,165)(145,166)(146,167)(147,168)(148,169)(149,170); 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*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 >;