Overview
- Group
- SmallGroup(1408,13836)
- Rank
- 4
- Schläfli Type
- {2,88,4}
- Vertices, edges, …
- 2, 88, 176, 4
- Order of s0s1s2s3
- 88
- 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 := ( 4, 13)( 5, 12)( 6, 11)( 7, 10)( 8, 9)( 15, 24)( 16, 23)( 17, 22)( 18, 21)( 19, 20)( 25, 36)( 26, 46)( 27, 45)( 28, 44)( 29, 43)( 30, 42)( 31, 41)( 32, 40)( 33, 39)( 34, 38)( 35, 37)( 47, 58)( 48, 68)( 49, 67)( 50, 66)( 51, 65)( 52, 64)( 53, 63)( 54, 62)( 55, 61)( 56, 60)( 57, 59)( 70, 79)( 71, 78)( 72, 77)( 73, 76)( 74, 75)( 81, 90)( 82, 89)( 83, 88)( 84, 87)( 85, 86)( 91,135)( 92,145)( 93,144)( 94,143)( 95,142)( 96,141)( 97,140)( 98,139)( 99,138)(100,137)(101,136)(102,146)(103,156)(104,155)(105,154)(106,153)(107,152)(108,151)(109,150)(110,149)(111,148)(112,147)(113,168)(114,178)(115,177)(116,176)(117,175)(118,174)(119,173)(120,172)(121,171)(122,170)(123,169)(124,157)(125,167)(126,166)(127,165)(128,164)(129,163)(130,162)(131,161)(132,160)(133,159)(134,158);; s2 := ( 3, 92)( 4, 91)( 5,101)( 6,100)( 7, 99)( 8, 98)( 9, 97)( 10, 96)( 11, 95)( 12, 94)( 13, 93)( 14,103)( 15,102)( 16,112)( 17,111)( 18,110)( 19,109)( 20,108)( 21,107)( 22,106)( 23,105)( 24,104)( 25,114)( 26,113)( 27,123)( 28,122)( 29,121)( 30,120)( 31,119)( 32,118)( 33,117)( 34,116)( 35,115)( 36,125)( 37,124)( 38,134)( 39,133)( 40,132)( 41,131)( 42,130)( 43,129)( 44,128)( 45,127)( 46,126)( 47,147)( 48,146)( 49,156)( 50,155)( 51,154)( 52,153)( 53,152)( 54,151)( 55,150)( 56,149)( 57,148)( 58,136)( 59,135)( 60,145)( 61,144)( 62,143)( 63,142)( 64,141)( 65,140)( 66,139)( 67,138)( 68,137)( 69,169)( 70,168)( 71,178)( 72,177)( 73,176)( 74,175)( 75,174)( 76,173)( 77,172)( 78,171)( 79,170)( 80,158)( 81,157)( 82,167)( 83,166)( 84,165)( 85,164)( 86,163)( 87,162)( 88,161)( 89,160)( 90,159);; s3 := ( 47, 58)( 48, 59)( 49, 60)( 50, 61)( 51, 62)( 52, 63)( 53, 64)( 54, 65)( 55, 66)( 56, 67)( 57, 68)( 69, 80)( 70, 81)( 71, 82)( 72, 83)( 73, 84)( 74, 85)( 75, 86)( 76, 87)( 77, 88)( 78, 89)( 79, 90)( 91,113)( 92,114)( 93,115)( 94,116)( 95,117)( 96,118)( 97,119)( 98,120)( 99,121)(100,122)(101,123)(102,124)(103,125)(104,126)(105,127)(106,128)(107,129)(108,130)(109,131)(110,132)(111,133)(112,134)(135,168)(136,169)(137,170)(138,171)(139,172)(140,173)(141,174)(142,175)(143,176)(144,177)(145,178)(146,157)(147,158)(148,159)(149,160)(150,161)(151,162)(152,163)(153,164)(154,165)(155,166)(156,167);; 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,
s2*s3*s2*s3*s2*s3*s2*s3, s1*s3*s2*s3*s2*s1*s2*s1*s3*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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s3*s2*s1*s2*s1*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*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(178)!(1,2); s1 := Sym(178)!( 4, 13)( 5, 12)( 6, 11)( 7, 10)( 8, 9)( 15, 24)( 16, 23)( 17, 22)( 18, 21)( 19, 20)( 25, 36)( 26, 46)( 27, 45)( 28, 44)( 29, 43)( 30, 42)( 31, 41)( 32, 40)( 33, 39)( 34, 38)( 35, 37)( 47, 58)( 48, 68)( 49, 67)( 50, 66)( 51, 65)( 52, 64)( 53, 63)( 54, 62)( 55, 61)( 56, 60)( 57, 59)( 70, 79)( 71, 78)( 72, 77)( 73, 76)( 74, 75)( 81, 90)( 82, 89)( 83, 88)( 84, 87)( 85, 86)( 91,135)( 92,145)( 93,144)( 94,143)( 95,142)( 96,141)( 97,140)( 98,139)( 99,138)(100,137)(101,136)(102,146)(103,156)(104,155)(105,154)(106,153)(107,152)(108,151)(109,150)(110,149)(111,148)(112,147)(113,168)(114,178)(115,177)(116,176)(117,175)(118,174)(119,173)(120,172)(121,171)(122,170)(123,169)(124,157)(125,167)(126,166)(127,165)(128,164)(129,163)(130,162)(131,161)(132,160)(133,159)(134,158); s2 := Sym(178)!( 3, 92)( 4, 91)( 5,101)( 6,100)( 7, 99)( 8, 98)( 9, 97)( 10, 96)( 11, 95)( 12, 94)( 13, 93)( 14,103)( 15,102)( 16,112)( 17,111)( 18,110)( 19,109)( 20,108)( 21,107)( 22,106)( 23,105)( 24,104)( 25,114)( 26,113)( 27,123)( 28,122)( 29,121)( 30,120)( 31,119)( 32,118)( 33,117)( 34,116)( 35,115)( 36,125)( 37,124)( 38,134)( 39,133)( 40,132)( 41,131)( 42,130)( 43,129)( 44,128)( 45,127)( 46,126)( 47,147)( 48,146)( 49,156)( 50,155)( 51,154)( 52,153)( 53,152)( 54,151)( 55,150)( 56,149)( 57,148)( 58,136)( 59,135)( 60,145)( 61,144)( 62,143)( 63,142)( 64,141)( 65,140)( 66,139)( 67,138)( 68,137)( 69,169)( 70,168)( 71,178)( 72,177)( 73,176)( 74,175)( 75,174)( 76,173)( 77,172)( 78,171)( 79,170)( 80,158)( 81,157)( 82,167)( 83,166)( 84,165)( 85,164)( 86,163)( 87,162)( 88,161)( 89,160)( 90,159); s3 := Sym(178)!( 47, 58)( 48, 59)( 49, 60)( 50, 61)( 51, 62)( 52, 63)( 53, 64)( 54, 65)( 55, 66)( 56, 67)( 57, 68)( 69, 80)( 70, 81)( 71, 82)( 72, 83)( 73, 84)( 74, 85)( 75, 86)( 76, 87)( 77, 88)( 78, 89)( 79, 90)( 91,113)( 92,114)( 93,115)( 94,116)( 95,117)( 96,118)( 97,119)( 98,120)( 99,121)(100,122)(101,123)(102,124)(103,125)(104,126)(105,127)(106,128)(107,129)(108,130)(109,131)(110,132)(111,133)(112,134)(135,168)(136,169)(137,170)(138,171)(139,172)(140,173)(141,174)(142,175)(143,176)(144,177)(145,178)(146,157)(147,158)(148,159)(149,160)(150,161)(151,162)(152,163)(153,164)(154,165)(155,166)(156,167); 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, s2*s3*s2*s3*s2*s3*s2*s3, s1*s3*s2*s3*s2*s1*s2*s1*s3*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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s3*s2*s1*s2*s1*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*s1*s2*s1*s2 >;