Overview
- Group
- SmallGroup(1408,17614)
- Rank
- 4
- Schläfli Type
- {2,16,22}
- Vertices, edges, …
- 2, 16, 176, 22
- Order of s0s1s2s3
- 176
- 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
4-fold
8-fold
11-fold
16-fold
22-fold
44-fold
88-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := ( 25, 36)( 26, 37)( 27, 38)( 28, 39)( 29, 40)( 30, 41)( 31, 42)( 32, 43)( 33, 44)( 34, 45)( 35, 46)( 47, 69)( 48, 70)( 49, 71)( 50, 72)( 51, 73)( 52, 74)( 53, 75)( 54, 76)( 55, 77)( 56, 78)( 57, 79)( 58, 80)( 59, 81)( 60, 82)( 61, 83)( 62, 84)( 63, 85)( 64, 86)( 65, 87)( 66, 88)( 67, 89)( 68, 90)( 91,135)( 92,136)( 93,137)( 94,138)( 95,139)( 96,140)( 97,141)( 98,142)( 99,143)(100,144)(101,145)(102,146)(103,147)(104,148)(105,149)(106,150)(107,151)(108,152)(109,153)(110,154)(111,155)(112,156)(113,168)(114,169)(115,170)(116,171)(117,172)(118,173)(119,174)(120,175)(121,176)(122,177)(123,178)(124,157)(125,158)(126,159)(127,160)(128,161)(129,162)(130,163)(131,164)(132,165)(133,166)(134,167);; s2 := ( 3, 91)( 4,101)( 5,100)( 6, 99)( 7, 98)( 8, 97)( 9, 96)( 10, 95)( 11, 94)( 12, 93)( 13, 92)( 14,102)( 15,112)( 16,111)( 17,110)( 18,109)( 19,108)( 20,107)( 21,106)( 22,105)( 23,104)( 24,103)( 25,124)( 26,134)( 27,133)( 28,132)( 29,131)( 30,130)( 31,129)( 32,128)( 33,127)( 34,126)( 35,125)( 36,113)( 37,123)( 38,122)( 39,121)( 40,120)( 41,119)( 42,118)( 43,117)( 44,116)( 45,115)( 46,114)( 47,157)( 48,167)( 49,166)( 50,165)( 51,164)( 52,163)( 53,162)( 54,161)( 55,160)( 56,159)( 57,158)( 58,168)( 59,178)( 60,177)( 61,176)( 62,175)( 63,174)( 64,173)( 65,172)( 66,171)( 67,170)( 68,169)( 69,135)( 70,145)( 71,144)( 72,143)( 73,142)( 74,141)( 75,140)( 76,139)( 77,138)( 78,137)( 79,136)( 80,146)( 81,156)( 82,155)( 83,154)( 84,153)( 85,152)( 86,151)( 87,150)( 88,149)( 89,148)( 90,147);; s3 := ( 3, 4)( 5, 13)( 6, 12)( 7, 11)( 8, 10)( 14, 15)( 16, 24)( 17, 23)( 18, 22)( 19, 21)( 25, 26)( 27, 35)( 28, 34)( 29, 33)( 30, 32)( 36, 37)( 38, 46)( 39, 45)( 40, 44)( 41, 43)( 47, 48)( 49, 57)( 50, 56)( 51, 55)( 52, 54)( 58, 59)( 60, 68)( 61, 67)( 62, 66)( 63, 65)( 69, 70)( 71, 79)( 72, 78)( 73, 77)( 74, 76)( 80, 81)( 82, 90)( 83, 89)( 84, 88)( 85, 87)( 91, 92)( 93,101)( 94,100)( 95, 99)( 96, 98)(102,103)(104,112)(105,111)(106,110)(107,109)(113,114)(115,123)(116,122)(117,121)(118,120)(124,125)(126,134)(127,133)(128,132)(129,131)(135,136)(137,145)(138,144)(139,143)(140,142)(146,147)(148,156)(149,155)(150,154)(151,153)(157,158)(159,167)(160,166)(161,165)(162,164)(168,169)(170,178)(171,177)(172,176)(173,175);; 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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*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*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(178)!(1,2); s1 := Sym(178)!( 25, 36)( 26, 37)( 27, 38)( 28, 39)( 29, 40)( 30, 41)( 31, 42)( 32, 43)( 33, 44)( 34, 45)( 35, 46)( 47, 69)( 48, 70)( 49, 71)( 50, 72)( 51, 73)( 52, 74)( 53, 75)( 54, 76)( 55, 77)( 56, 78)( 57, 79)( 58, 80)( 59, 81)( 60, 82)( 61, 83)( 62, 84)( 63, 85)( 64, 86)( 65, 87)( 66, 88)( 67, 89)( 68, 90)( 91,135)( 92,136)( 93,137)( 94,138)( 95,139)( 96,140)( 97,141)( 98,142)( 99,143)(100,144)(101,145)(102,146)(103,147)(104,148)(105,149)(106,150)(107,151)(108,152)(109,153)(110,154)(111,155)(112,156)(113,168)(114,169)(115,170)(116,171)(117,172)(118,173)(119,174)(120,175)(121,176)(122,177)(123,178)(124,157)(125,158)(126,159)(127,160)(128,161)(129,162)(130,163)(131,164)(132,165)(133,166)(134,167); s2 := Sym(178)!( 3, 91)( 4,101)( 5,100)( 6, 99)( 7, 98)( 8, 97)( 9, 96)( 10, 95)( 11, 94)( 12, 93)( 13, 92)( 14,102)( 15,112)( 16,111)( 17,110)( 18,109)( 19,108)( 20,107)( 21,106)( 22,105)( 23,104)( 24,103)( 25,124)( 26,134)( 27,133)( 28,132)( 29,131)( 30,130)( 31,129)( 32,128)( 33,127)( 34,126)( 35,125)( 36,113)( 37,123)( 38,122)( 39,121)( 40,120)( 41,119)( 42,118)( 43,117)( 44,116)( 45,115)( 46,114)( 47,157)( 48,167)( 49,166)( 50,165)( 51,164)( 52,163)( 53,162)( 54,161)( 55,160)( 56,159)( 57,158)( 58,168)( 59,178)( 60,177)( 61,176)( 62,175)( 63,174)( 64,173)( 65,172)( 66,171)( 67,170)( 68,169)( 69,135)( 70,145)( 71,144)( 72,143)( 73,142)( 74,141)( 75,140)( 76,139)( 77,138)( 78,137)( 79,136)( 80,146)( 81,156)( 82,155)( 83,154)( 84,153)( 85,152)( 86,151)( 87,150)( 88,149)( 89,148)( 90,147); s3 := Sym(178)!( 3, 4)( 5, 13)( 6, 12)( 7, 11)( 8, 10)( 14, 15)( 16, 24)( 17, 23)( 18, 22)( 19, 21)( 25, 26)( 27, 35)( 28, 34)( 29, 33)( 30, 32)( 36, 37)( 38, 46)( 39, 45)( 40, 44)( 41, 43)( 47, 48)( 49, 57)( 50, 56)( 51, 55)( 52, 54)( 58, 59)( 60, 68)( 61, 67)( 62, 66)( 63, 65)( 69, 70)( 71, 79)( 72, 78)( 73, 77)( 74, 76)( 80, 81)( 82, 90)( 83, 89)( 84, 88)( 85, 87)( 91, 92)( 93,101)( 94,100)( 95, 99)( 96, 98)(102,103)(104,112)(105,111)(106,110)(107,109)(113,114)(115,123)(116,122)(117,121)(118,120)(124,125)(126,134)(127,133)(128,132)(129,131)(135,136)(137,145)(138,144)(139,143)(140,142)(146,147)(148,156)(149,155)(150,154)(151,153)(157,158)(159,167)(160,166)(161,165)(162,164)(168,169)(170,178)(171,177)(172,176)(173,175); poly := sub<Sym(178)|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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*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*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;