Overview
- Group
- SmallGroup(1408,13895)
- Rank
- 4
- Schläfli Type
- {4,44,2}
- Vertices, edges, …
- 8, 176, 88, 2
- Order of s0s1s2s3
- 44
- 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 := ( 45, 56)( 46, 57)( 47, 58)( 48, 59)( 49, 60)( 50, 61)( 51, 62)( 52, 63)( 53, 64)( 54, 65)( 55, 66)( 67, 78)( 68, 79)( 69, 80)( 70, 81)( 71, 82)( 72, 83)( 73, 84)( 74, 85)( 75, 86)( 76, 87)( 77, 88)( 89,111)( 90,112)( 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)(133,166)(134,167)(135,168)(136,169)(137,170)(138,171)(139,172)(140,173)(141,174)(142,175)(143,176)(144,155)(145,156)(146,157)(147,158)(148,159)(149,160)(150,161)(151,162)(152,163)(153,164)(154,165);; s1 := ( 1, 89)( 2, 99)( 3, 98)( 4, 97)( 5, 96)( 6, 95)( 7, 94)( 8, 93)( 9, 92)( 10, 91)( 11, 90)( 12,100)( 13,110)( 14,109)( 15,108)( 16,107)( 17,106)( 18,105)( 19,104)( 20,103)( 21,102)( 22,101)( 23,111)( 24,121)( 25,120)( 26,119)( 27,118)( 28,117)( 29,116)( 30,115)( 31,114)( 32,113)( 33,112)( 34,122)( 35,132)( 36,131)( 37,130)( 38,129)( 39,128)( 40,127)( 41,126)( 42,125)( 43,124)( 44,123)( 45,133)( 46,143)( 47,142)( 48,141)( 49,140)( 50,139)( 51,138)( 52,137)( 53,136)( 54,135)( 55,134)( 56,144)( 57,154)( 58,153)( 59,152)( 60,151)( 61,150)( 62,149)( 63,148)( 64,147)( 65,146)( 66,145)( 67,155)( 68,165)( 69,164)( 70,163)( 71,162)( 72,161)( 73,160)( 74,159)( 75,158)( 76,157)( 77,156)( 78,166)( 79,176)( 80,175)( 81,174)( 82,173)( 83,172)( 84,171)( 85,170)( 86,169)( 87,168)( 88,167);; s2 := ( 1, 2)( 3, 11)( 4, 10)( 5, 9)( 6, 8)( 12, 13)( 14, 22)( 15, 21)( 16, 20)( 17, 19)( 23, 35)( 24, 34)( 25, 44)( 26, 43)( 27, 42)( 28, 41)( 29, 40)( 30, 39)( 31, 38)( 32, 37)( 33, 36)( 45, 46)( 47, 55)( 48, 54)( 49, 53)( 50, 52)( 56, 57)( 58, 66)( 59, 65)( 60, 64)( 61, 63)( 67, 79)( 68, 78)( 69, 88)( 70, 87)( 71, 86)( 72, 85)( 73, 84)( 74, 83)( 75, 82)( 76, 81)( 77, 80)( 89,134)( 90,133)( 91,143)( 92,142)( 93,141)( 94,140)( 95,139)( 96,138)( 97,137)( 98,136)( 99,135)(100,145)(101,144)(102,154)(103,153)(104,152)(105,151)(106,150)(107,149)(108,148)(109,147)(110,146)(111,167)(112,166)(113,176)(114,175)(115,174)(116,173)(117,172)(118,171)(119,170)(120,169)(121,168)(122,156)(123,155)(124,165)(125,164)(126,163)(127,162)(128,161)(129,160)(130,159)(131,158)(132,157);; s3 := (177,178);; 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*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3,
s0*s1*s0*s1*s0*s1*s0*s1, s1*s2*s0*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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)!( 45, 56)( 46, 57)( 47, 58)( 48, 59)( 49, 60)( 50, 61)( 51, 62)( 52, 63)( 53, 64)( 54, 65)( 55, 66)( 67, 78)( 68, 79)( 69, 80)( 70, 81)( 71, 82)( 72, 83)( 73, 84)( 74, 85)( 75, 86)( 76, 87)( 77, 88)( 89,111)( 90,112)( 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)(133,166)(134,167)(135,168)(136,169)(137,170)(138,171)(139,172)(140,173)(141,174)(142,175)(143,176)(144,155)(145,156)(146,157)(147,158)(148,159)(149,160)(150,161)(151,162)(152,163)(153,164)(154,165); s1 := Sym(178)!( 1, 89)( 2, 99)( 3, 98)( 4, 97)( 5, 96)( 6, 95)( 7, 94)( 8, 93)( 9, 92)( 10, 91)( 11, 90)( 12,100)( 13,110)( 14,109)( 15,108)( 16,107)( 17,106)( 18,105)( 19,104)( 20,103)( 21,102)( 22,101)( 23,111)( 24,121)( 25,120)( 26,119)( 27,118)( 28,117)( 29,116)( 30,115)( 31,114)( 32,113)( 33,112)( 34,122)( 35,132)( 36,131)( 37,130)( 38,129)( 39,128)( 40,127)( 41,126)( 42,125)( 43,124)( 44,123)( 45,133)( 46,143)( 47,142)( 48,141)( 49,140)( 50,139)( 51,138)( 52,137)( 53,136)( 54,135)( 55,134)( 56,144)( 57,154)( 58,153)( 59,152)( 60,151)( 61,150)( 62,149)( 63,148)( 64,147)( 65,146)( 66,145)( 67,155)( 68,165)( 69,164)( 70,163)( 71,162)( 72,161)( 73,160)( 74,159)( 75,158)( 76,157)( 77,156)( 78,166)( 79,176)( 80,175)( 81,174)( 82,173)( 83,172)( 84,171)( 85,170)( 86,169)( 87,168)( 88,167); s2 := Sym(178)!( 1, 2)( 3, 11)( 4, 10)( 5, 9)( 6, 8)( 12, 13)( 14, 22)( 15, 21)( 16, 20)( 17, 19)( 23, 35)( 24, 34)( 25, 44)( 26, 43)( 27, 42)( 28, 41)( 29, 40)( 30, 39)( 31, 38)( 32, 37)( 33, 36)( 45, 46)( 47, 55)( 48, 54)( 49, 53)( 50, 52)( 56, 57)( 58, 66)( 59, 65)( 60, 64)( 61, 63)( 67, 79)( 68, 78)( 69, 88)( 70, 87)( 71, 86)( 72, 85)( 73, 84)( 74, 83)( 75, 82)( 76, 81)( 77, 80)( 89,134)( 90,133)( 91,143)( 92,142)( 93,141)( 94,140)( 95,139)( 96,138)( 97,137)( 98,136)( 99,135)(100,145)(101,144)(102,154)(103,153)(104,152)(105,151)(106,150)(107,149)(108,148)(109,147)(110,146)(111,167)(112,166)(113,176)(114,175)(115,174)(116,173)(117,172)(118,171)(119,170)(120,169)(121,168)(122,156)(123,155)(124,165)(125,164)(126,163)(127,162)(128,161)(129,160)(130,159)(131,158)(132,157); s3 := Sym(178)!(177,178); 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*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1, s1*s2*s0*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;