Overview
- Group
- SmallGroup(1344,10867)
- Rank
- 4
- Schläfli Type
- {2,84,4}
- Vertices, edges, …
- 2, 84, 168, 4
- 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
8-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)( 10, 17)( 11, 23)( 12, 22)( 13, 21)( 14, 20)( 15, 19)( 16, 18)( 25, 30)( 26, 29)( 27, 28)( 31, 38)( 32, 44)( 33, 43)( 34, 42)( 35, 41)( 36, 40)( 37, 39)( 46, 51)( 47, 50)( 48, 49)( 52, 59)( 53, 65)( 54, 64)( 55, 63)( 56, 62)( 57, 61)( 58, 60)( 67, 72)( 68, 71)( 69, 70)( 73, 80)( 74, 86)( 75, 85)( 76, 84)( 77, 83)( 78, 82)( 79, 81)( 87,129)( 88,135)( 89,134)( 90,133)( 91,132)( 92,131)( 93,130)( 94,143)( 95,149)( 96,148)( 97,147)( 98,146)( 99,145)(100,144)(101,136)(102,142)(103,141)(104,140)(105,139)(106,138)(107,137)(108,150)(109,156)(110,155)(111,154)(112,153)(113,152)(114,151)(115,164)(116,170)(117,169)(118,168)(119,167)(120,166)(121,165)(122,157)(123,163)(124,162)(125,161)(126,160)(127,159)(128,158);; s2 := ( 3, 95)( 4, 94)( 5,100)( 6, 99)( 7, 98)( 8, 97)( 9, 96)( 10, 88)( 11, 87)( 12, 93)( 13, 92)( 14, 91)( 15, 90)( 16, 89)( 17,102)( 18,101)( 19,107)( 20,106)( 21,105)( 22,104)( 23,103)( 24,116)( 25,115)( 26,121)( 27,120)( 28,119)( 29,118)( 30,117)( 31,109)( 32,108)( 33,114)( 34,113)( 35,112)( 36,111)( 37,110)( 38,123)( 39,122)( 40,128)( 41,127)( 42,126)( 43,125)( 44,124)( 45,137)( 46,136)( 47,142)( 48,141)( 49,140)( 50,139)( 51,138)( 52,130)( 53,129)( 54,135)( 55,134)( 56,133)( 57,132)( 58,131)( 59,144)( 60,143)( 61,149)( 62,148)( 63,147)( 64,146)( 65,145)( 66,158)( 67,157)( 68,163)( 69,162)( 70,161)( 71,160)( 72,159)( 73,151)( 74,150)( 75,156)( 76,155)( 77,154)( 78,153)( 79,152)( 80,165)( 81,164)( 82,170)( 83,169)( 84,168)( 85,167)( 86,166);; s3 := ( 87,108)( 88,109)( 89,110)( 90,111)( 91,112)( 92,113)( 93,114)( 94,115)( 95,116)( 96,117)( 97,118)( 98,119)( 99,120)(100,121)(101,122)(102,123)(103,124)(104,125)(105,126)(106,127)(107,128)(129,150)(130,151)(131,152)(132,153)(133,154)(134,155)(135,156)(136,157)(137,158)(138,159)(139,160)(140,161)(141,162)(142,163)(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,
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*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)( 10, 17)( 11, 23)( 12, 22)( 13, 21)( 14, 20)( 15, 19)( 16, 18)( 25, 30)( 26, 29)( 27, 28)( 31, 38)( 32, 44)( 33, 43)( 34, 42)( 35, 41)( 36, 40)( 37, 39)( 46, 51)( 47, 50)( 48, 49)( 52, 59)( 53, 65)( 54, 64)( 55, 63)( 56, 62)( 57, 61)( 58, 60)( 67, 72)( 68, 71)( 69, 70)( 73, 80)( 74, 86)( 75, 85)( 76, 84)( 77, 83)( 78, 82)( 79, 81)( 87,129)( 88,135)( 89,134)( 90,133)( 91,132)( 92,131)( 93,130)( 94,143)( 95,149)( 96,148)( 97,147)( 98,146)( 99,145)(100,144)(101,136)(102,142)(103,141)(104,140)(105,139)(106,138)(107,137)(108,150)(109,156)(110,155)(111,154)(112,153)(113,152)(114,151)(115,164)(116,170)(117,169)(118,168)(119,167)(120,166)(121,165)(122,157)(123,163)(124,162)(125,161)(126,160)(127,159)(128,158); s2 := Sym(170)!( 3, 95)( 4, 94)( 5,100)( 6, 99)( 7, 98)( 8, 97)( 9, 96)( 10, 88)( 11, 87)( 12, 93)( 13, 92)( 14, 91)( 15, 90)( 16, 89)( 17,102)( 18,101)( 19,107)( 20,106)( 21,105)( 22,104)( 23,103)( 24,116)( 25,115)( 26,121)( 27,120)( 28,119)( 29,118)( 30,117)( 31,109)( 32,108)( 33,114)( 34,113)( 35,112)( 36,111)( 37,110)( 38,123)( 39,122)( 40,128)( 41,127)( 42,126)( 43,125)( 44,124)( 45,137)( 46,136)( 47,142)( 48,141)( 49,140)( 50,139)( 51,138)( 52,130)( 53,129)( 54,135)( 55,134)( 56,133)( 57,132)( 58,131)( 59,144)( 60,143)( 61,149)( 62,148)( 63,147)( 64,146)( 65,145)( 66,158)( 67,157)( 68,163)( 69,162)( 70,161)( 71,160)( 72,159)( 73,151)( 74,150)( 75,156)( 76,155)( 77,154)( 78,153)( 79,152)( 80,165)( 81,164)( 82,170)( 83,169)( 84,168)( 85,167)( 86,166); s3 := Sym(170)!( 87,108)( 88,109)( 89,110)( 90,111)( 91,112)( 92,113)( 93,114)( 94,115)( 95,116)( 96,117)( 97,118)( 98,119)( 99,120)(100,121)(101,122)(102,123)(103,124)(104,125)(105,126)(106,127)(107,128)(129,150)(130,151)(131,152)(132,153)(133,154)(134,155)(135,156)(136,157)(137,158)(138,159)(139,160)(140,161)(141,162)(142,163)(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, 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*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 >;