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# Polytope of Type {118,4}

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

```
References : None.
to this polytope