Polytope of Type {4,118}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,118}*944
Also Known As : {4,118|2}. if this polytope has another name.
Group : SmallGroup(944,31)
Rank : 3
Schlafli Type : {4,118}
Number of vertices, edges, etc : 4, 236, 118
Order of s0s1s2 : 236
Order of s0s1s2s1 : 2
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{4,118,2} of size 1888
Vertex Figure Of :
{2,4,118} of size 1888
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2,118}*472
4-fold quotients : {2,59}*236
59-fold quotients : {4,2}*16
118-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
2-fold covers : {4,236}*1888, {8,118}*1888
Permutation Representation (GAP) :
s0 := (119,178)(120,179)(121,180)(122,181)(123,182)(124,183)(125,184)(126,185)
(127,186)(128,187)(129,188)(130,189)(131,190)(132,191)(133,192)(134,193)
(135,194)(136,195)(137,196)(138,197)(139,198)(140,199)(141,200)(142,201)
(143,202)(144,203)(145,204)(146,205)(147,206)(148,207)(149,208)(150,209)
(151,210)(152,211)(153,212)(154,213)(155,214)(156,215)(157,216)(158,217)
(159,218)(160,219)(161,220)(162,221)(163,222)(164,223)(165,224)(166,225)
(167,226)(168,227)(169,228)(170,229)(171,230)(172,231)(173,232)(174,233)
(175,234)(176,235)(177,236);;
s1 := ( 1,119)( 2,177)( 3,176)( 4,175)( 5,174)( 6,173)( 7,172)( 8,171)
( 9,170)( 10,169)( 11,168)( 12,167)( 13,166)( 14,165)( 15,164)( 16,163)
( 17,162)( 18,161)( 19,160)( 20,159)( 21,158)( 22,157)( 23,156)( 24,155)
( 25,154)( 26,153)( 27,152)( 28,151)( 29,150)( 30,149)( 31,148)( 32,147)
( 33,146)( 34,145)( 35,144)( 36,143)( 37,142)( 38,141)( 39,140)( 40,139)
( 41,138)( 42,137)( 43,136)( 44,135)( 45,134)( 46,133)( 47,132)( 48,131)
( 49,130)( 50,129)( 51,128)( 52,127)( 53,126)( 54,125)( 55,124)( 56,123)
( 57,122)( 58,121)( 59,120)( 60,178)( 61,236)( 62,235)( 63,234)( 64,233)
( 65,232)( 66,231)( 67,230)( 68,229)( 69,228)( 70,227)( 71,226)( 72,225)
( 73,224)( 74,223)( 75,222)( 76,221)( 77,220)( 78,219)( 79,218)( 80,217)
( 81,216)( 82,215)( 83,214)( 84,213)( 85,212)( 86,211)( 87,210)( 88,209)
( 89,208)( 90,207)( 91,206)( 92,205)( 93,204)( 94,203)( 95,202)( 96,201)
( 97,200)( 98,199)( 99,198)(100,197)(101,196)(102,195)(103,194)(104,193)
(105,192)(106,191)(107,190)(108,189)(109,188)(110,187)(111,186)(112,185)
(113,184)(114,183)(115,182)(116,181)(117,180)(118,179);;
s2 := ( 1, 2)( 3, 59)( 4, 58)( 5, 57)( 6, 56)( 7, 55)( 8, 54)( 9, 53)
( 10, 52)( 11, 51)( 12, 50)( 13, 49)( 14, 48)( 15, 47)( 16, 46)( 17, 45)
( 18, 44)( 19, 43)( 20, 42)( 21, 41)( 22, 40)( 23, 39)( 24, 38)( 25, 37)
( 26, 36)( 27, 35)( 28, 34)( 29, 33)( 30, 32)( 60, 61)( 62,118)( 63,117)
( 64,116)( 65,115)( 66,114)( 67,113)( 68,112)( 69,111)( 70,110)( 71,109)
( 72,108)( 73,107)( 74,106)( 75,105)( 76,104)( 77,103)( 78,102)( 79,101)
( 80,100)( 81, 99)( 82, 98)( 83, 97)( 84, 96)( 85, 95)( 86, 94)( 87, 93)
( 88, 92)( 89, 91)(119,120)(121,177)(122,176)(123,175)(124,174)(125,173)
(126,172)(127,171)(128,170)(129,169)(130,168)(131,167)(132,166)(133,165)
(134,164)(135,163)(136,162)(137,161)(138,160)(139,159)(140,158)(141,157)
(142,156)(143,155)(144,154)(145,153)(146,152)(147,151)(148,150)(178,179)
(180,236)(181,235)(182,234)(183,233)(184,232)(185,231)(186,230)(187,229)
(188,228)(189,227)(190,226)(191,225)(192,224)(193,223)(194,222)(195,221)
(196,220)(197,219)(198,218)(199,217)(200,216)(201,215)(202,214)(203,213)
(204,212)(205,211)(206,210)(207,209);;
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, 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*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*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(236)!(119,178)(120,179)(121,180)(122,181)(123,182)(124,183)(125,184)
(126,185)(127,186)(128,187)(129,188)(130,189)(131,190)(132,191)(133,192)
(134,193)(135,194)(136,195)(137,196)(138,197)(139,198)(140,199)(141,200)
(142,201)(143,202)(144,203)(145,204)(146,205)(147,206)(148,207)(149,208)
(150,209)(151,210)(152,211)(153,212)(154,213)(155,214)(156,215)(157,216)
(158,217)(159,218)(160,219)(161,220)(162,221)(163,222)(164,223)(165,224)
(166,225)(167,226)(168,227)(169,228)(170,229)(171,230)(172,231)(173,232)
(174,233)(175,234)(176,235)(177,236);
s1 := Sym(236)!( 1,119)( 2,177)( 3,176)( 4,175)( 5,174)( 6,173)( 7,172)
( 8,171)( 9,170)( 10,169)( 11,168)( 12,167)( 13,166)( 14,165)( 15,164)
( 16,163)( 17,162)( 18,161)( 19,160)( 20,159)( 21,158)( 22,157)( 23,156)
( 24,155)( 25,154)( 26,153)( 27,152)( 28,151)( 29,150)( 30,149)( 31,148)
( 32,147)( 33,146)( 34,145)( 35,144)( 36,143)( 37,142)( 38,141)( 39,140)
( 40,139)( 41,138)( 42,137)( 43,136)( 44,135)( 45,134)( 46,133)( 47,132)
( 48,131)( 49,130)( 50,129)( 51,128)( 52,127)( 53,126)( 54,125)( 55,124)
( 56,123)( 57,122)( 58,121)( 59,120)( 60,178)( 61,236)( 62,235)( 63,234)
( 64,233)( 65,232)( 66,231)( 67,230)( 68,229)( 69,228)( 70,227)( 71,226)
( 72,225)( 73,224)( 74,223)( 75,222)( 76,221)( 77,220)( 78,219)( 79,218)
( 80,217)( 81,216)( 82,215)( 83,214)( 84,213)( 85,212)( 86,211)( 87,210)
( 88,209)( 89,208)( 90,207)( 91,206)( 92,205)( 93,204)( 94,203)( 95,202)
( 96,201)( 97,200)( 98,199)( 99,198)(100,197)(101,196)(102,195)(103,194)
(104,193)(105,192)(106,191)(107,190)(108,189)(109,188)(110,187)(111,186)
(112,185)(113,184)(114,183)(115,182)(116,181)(117,180)(118,179);
s2 := Sym(236)!( 1, 2)( 3, 59)( 4, 58)( 5, 57)( 6, 56)( 7, 55)( 8, 54)
( 9, 53)( 10, 52)( 11, 51)( 12, 50)( 13, 49)( 14, 48)( 15, 47)( 16, 46)
( 17, 45)( 18, 44)( 19, 43)( 20, 42)( 21, 41)( 22, 40)( 23, 39)( 24, 38)
( 25, 37)( 26, 36)( 27, 35)( 28, 34)( 29, 33)( 30, 32)( 60, 61)( 62,118)
( 63,117)( 64,116)( 65,115)( 66,114)( 67,113)( 68,112)( 69,111)( 70,110)
( 71,109)( 72,108)( 73,107)( 74,106)( 75,105)( 76,104)( 77,103)( 78,102)
( 79,101)( 80,100)( 81, 99)( 82, 98)( 83, 97)( 84, 96)( 85, 95)( 86, 94)
( 87, 93)( 88, 92)( 89, 91)(119,120)(121,177)(122,176)(123,175)(124,174)
(125,173)(126,172)(127,171)(128,170)(129,169)(130,168)(131,167)(132,166)
(133,165)(134,164)(135,163)(136,162)(137,161)(138,160)(139,159)(140,158)
(141,157)(142,156)(143,155)(144,154)(145,153)(146,152)(147,151)(148,150)
(178,179)(180,236)(181,235)(182,234)(183,233)(184,232)(185,231)(186,230)
(187,229)(188,228)(189,227)(190,226)(191,225)(192,224)(193,223)(194,222)
(195,221)(196,220)(197,219)(198,218)(199,217)(200,216)(201,215)(202,214)
(203,213)(204,212)(205,211)(206,210)(207,209);
poly := sub<Sym(236)|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, 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*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*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