Overview
- Group
- SmallGroup(1408,6495)
- Rank
- 3
- Schläfli Type
- {4,88}
- Vertices, edges, …
- 8, 352, 176
- 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 := ( 45, 78)( 46, 79)( 47, 80)( 48, 81)( 49, 82)( 50, 83)( 51, 84)( 52, 85)( 53, 86)( 54, 87)( 55, 88)( 56, 67)( 57, 68)( 58, 69)( 59, 70)( 60, 71)( 61, 72)( 62, 73)( 63, 74)( 64, 75)( 65, 76)( 66, 77)(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 := ( 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, 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)( 45,167)( 46,166)( 47,176)( 48,175)( 49,174)( 50,173)( 51,172)( 52,171)( 53,170)( 54,169)( 55,168)( 56,156)( 57,155)( 58,165)( 59,164)( 60,163)( 61,162)( 62,161)( 63,160)( 64,159)( 65,158)( 66,157)( 67,145)( 68,144)( 69,154)( 70,153)( 71,152)( 72,151)( 73,150)( 74,149)( 75,148)( 76,147)( 77,146)( 78,134)( 79,133)( 80,143)( 81,142)( 82,141)( 83,140)( 84,139)( 85,138)( 86,137)( 87,136)( 88,135);; 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*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1,
s0*s1*s2*s1*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*s0*s2*s1*s0*s2*s1*s0*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*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(176)!( 45, 78)( 46, 79)( 47, 80)( 48, 81)( 49, 82)( 50, 83)( 51, 84)( 52, 85)( 53, 86)( 54, 87)( 55, 88)( 56, 67)( 57, 68)( 58, 69)( 59, 70)( 60, 71)( 61, 72)( 62, 73)( 63, 74)( 64, 75)( 65, 76)( 66, 77)(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(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, 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)( 45,167)( 46,166)( 47,176)( 48,175)( 49,174)( 50,173)( 51,172)( 52,171)( 53,170)( 54,169)( 55,168)( 56,156)( 57,155)( 58,165)( 59,164)( 60,163)( 61,162)( 62,161)( 63,160)( 64,159)( 65,158)( 66,157)( 67,145)( 68,144)( 69,154)( 70,153)( 71,152)( 72,151)( 73,150)( 74,149)( 75,148)( 76,147)( 77,146)( 78,134)( 79,133)( 80,143)( 81,142)( 82,141)( 83,140)( 84,139)( 85,138)( 86,137)( 87,136)( 88,135); 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*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, s0*s1*s2*s1*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*s0*s2*s1*s0*s2*s1*s0*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*s0*s1 >;
References
None.
to this polytope.