Overview
- Group
- SmallGroup(1408,6496)
- Rank
- 3
- Schläfli Type
- {8,44}
- Vertices, edges, …
- 16, 352, 88
- Order of s0s1s2
- 44
- Order of s0s1s2s1
- 4
- Also known as
- if this polytope has a name.
Special Properties
- Compact Hyperbolic Quotient
- Locally Spherical
- Orientable
Quotients maximal quotients in bold
2-fold
4-fold
8-fold
11-fold
16-fold
22-fold
32-fold
44-fold
88-fold
176-fold
Covers minimal covers in bold
None in this atlas.
Irregular Quotients of which this is a minimal cover
Click an entry to reveal its facets and vertex figures.
Representations
Permutation Representation (GAP)
s0 := ( 1, 89)( 2, 90)( 3, 91)( 4, 92)( 5, 93)( 6, 94)( 7, 95)( 8, 96)( 9, 97)( 10, 98)( 11, 99)( 12,100)( 13,101)( 14,102)( 15,103)( 16,104)( 17,105)( 18,106)( 19,107)( 20,108)( 21,109)( 22,110)( 23,111)( 24,112)( 25,113)( 26,114)( 27,115)( 28,116)( 29,117)( 30,118)( 31,119)( 32,120)( 33,121)( 34,122)( 35,123)( 36,124)( 37,125)( 38,126)( 39,127)( 40,128)( 41,129)( 42,130)( 43,131)( 44,132)( 45,166)( 46,167)( 47,168)( 48,169)( 49,170)( 50,171)( 51,172)( 52,173)( 53,174)( 54,175)( 55,176)( 56,155)( 57,156)( 58,157)( 59,158)( 60,159)( 61,160)( 62,161)( 63,162)( 64,163)( 65,164)( 66,165)( 67,144)( 68,145)( 69,146)( 70,147)( 71,148)( 72,149)( 73,150)( 74,151)( 75,152)( 76,153)( 77,154)( 78,133)( 79,134)( 80,135)( 81,136)( 82,137)( 83,138)( 84,139)( 85,140)( 86,141)( 87,142)( 88,143);; s1 := ( 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);; s2 := ( 1, 2)( 3, 11)( 4, 10)( 5, 9)( 6, 8)( 12, 13)( 14, 22)( 15, 21)( 16, 20)( 17, 19)( 23, 24)( 25, 33)( 26, 32)( 27, 31)( 28, 30)( 34, 35)( 36, 44)( 37, 43)( 38, 42)( 39, 41)( 45, 79)( 46, 78)( 47, 88)( 48, 87)( 49, 86)( 50, 85)( 51, 84)( 52, 83)( 53, 82)( 54, 81)( 55, 80)( 56, 68)( 57, 67)( 58, 77)( 59, 76)( 60, 75)( 61, 74)( 62, 73)( 63, 72)( 64, 71)( 65, 70)( 66, 69)( 89, 90)( 91, 99)( 92, 98)( 93, 97)( 94, 96)(100,101)(102,110)(103,109)(104,108)(105,107)(111,112)(113,121)(114,120)(115,119)(116,118)(122,123)(124,132)(125,131)(126,130)(127,129)(133,167)(134,166)(135,176)(136,175)(137,174)(138,173)(139,172)(140,171)(141,170)(142,169)(143,168)(144,156)(145,155)(146,165)(147,164)(148,163)(149,162)(150,161)(151,160)(152,159)(153,158)(154,157);; poly := Group([s0,s1,s2]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1","s2");;
s0 := F.1;; s1 := F.2;; s2 := F.3;;
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s2*s1*s2*s1*s0*s1*s0*s2*s1*s0*s2*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1,
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(176)!( 1, 89)( 2, 90)( 3, 91)( 4, 92)( 5, 93)( 6, 94)( 7, 95)( 8, 96)( 9, 97)( 10, 98)( 11, 99)( 12,100)( 13,101)( 14,102)( 15,103)( 16,104)( 17,105)( 18,106)( 19,107)( 20,108)( 21,109)( 22,110)( 23,111)( 24,112)( 25,113)( 26,114)( 27,115)( 28,116)( 29,117)( 30,118)( 31,119)( 32,120)( 33,121)( 34,122)( 35,123)( 36,124)( 37,125)( 38,126)( 39,127)( 40,128)( 41,129)( 42,130)( 43,131)( 44,132)( 45,166)( 46,167)( 47,168)( 48,169)( 49,170)( 50,171)( 51,172)( 52,173)( 53,174)( 54,175)( 55,176)( 56,155)( 57,156)( 58,157)( 59,158)( 60,159)( 61,160)( 62,161)( 63,162)( 64,163)( 65,164)( 66,165)( 67,144)( 68,145)( 69,146)( 70,147)( 71,148)( 72,149)( 73,150)( 74,151)( 75,152)( 76,153)( 77,154)( 78,133)( 79,134)( 80,135)( 81,136)( 82,137)( 83,138)( 84,139)( 85,140)( 86,141)( 87,142)( 88,143); s1 := Sym(176)!( 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); s2 := Sym(176)!( 1, 2)( 3, 11)( 4, 10)( 5, 9)( 6, 8)( 12, 13)( 14, 22)( 15, 21)( 16, 20)( 17, 19)( 23, 24)( 25, 33)( 26, 32)( 27, 31)( 28, 30)( 34, 35)( 36, 44)( 37, 43)( 38, 42)( 39, 41)( 45, 79)( 46, 78)( 47, 88)( 48, 87)( 49, 86)( 50, 85)( 51, 84)( 52, 83)( 53, 82)( 54, 81)( 55, 80)( 56, 68)( 57, 67)( 58, 77)( 59, 76)( 60, 75)( 61, 74)( 62, 73)( 63, 72)( 64, 71)( 65, 70)( 66, 69)( 89, 90)( 91, 99)( 92, 98)( 93, 97)( 94, 96)(100,101)(102,110)(103,109)(104,108)(105,107)(111,112)(113,121)(114,120)(115,119)(116,118)(122,123)(124,132)(125,131)(126,130)(127,129)(133,167)(134,166)(135,176)(136,175)(137,174)(138,173)(139,172)(140,171)(141,170)(142,169)(143,168)(144,156)(145,155)(146,165)(147,164)(148,163)(149,162)(150,161)(151,160)(152,159)(153,158)(154,157); poly := sub<Sym(176)|s0,s1,s2>;
Finitely Presented Group Representation (Magma)
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s2*s1*s2*s1*s0*s1*s0*s2*s1*s0*s2*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1, 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 >;
References
None.
to this polytope.