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