Polytope of Type {2,116,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,116,4}*1856
if this polytope has a name.
Group : SmallGroup(1856,1036)
Rank : 4
Schlafli Type : {2,116,4}
Number of vertices, edges, etc : 2, 116, 232, 4
Order of s₀s₁s₂s₃ : 116
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,116,2}*928, {2,58,4}*928
   4-fold quotients : {2,58,2}*464
   8-fold quotients : {2,29,2}*232
   29-fold quotients : {2,4,4}*64
   58-fold quotients : {2,2,4}*32, {2,4,2}*32
   116-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (  4, 31)(  5, 30)(  6, 29)(  7, 28)(  8, 27)(  9, 26)( 10, 25)( 11, 24)
( 12, 23)( 13, 22)( 14, 21)( 15, 20)( 16, 19)( 17, 18)( 33, 60)( 34, 59)
( 35, 58)( 36, 57)( 37, 56)( 38, 55)( 39, 54)( 40, 53)( 41, 52)( 42, 51)
( 43, 50)( 44, 49)( 45, 48)( 46, 47)( 62, 89)( 63, 88)( 64, 87)( 65, 86)
( 66, 85)( 67, 84)( 68, 83)( 69, 82)( 70, 81)( 71, 80)( 72, 79)( 73, 78)
( 74, 77)( 75, 76)( 91,118)( 92,117)( 93,116)( 94,115)( 95,114)( 96,113)
( 97,112)( 98,111)( 99,110)(100,109)(101,108)(102,107)(103,106)(104,105)
(119,177)(120,205)(121,204)(122,203)(123,202)(124,201)(125,200)(126,199)
(127,198)(128,197)(129,196)(130,195)(131,194)(132,193)(133,192)(134,191)
(135,190)(136,189)(137,188)(138,187)(139,186)(140,185)(141,184)(142,183)
(143,182)(144,181)(145,180)(146,179)(147,178)(148,206)(149,234)(150,233)
(151,232)(152,231)(153,230)(154,229)(155,228)(156,227)(157,226)(158,225)
(159,224)(160,223)(161,222)(162,221)(163,220)(164,219)(165,218)(166,217)
(167,216)(168,215)(169,214)(170,213)(171,212)(172,211)(173,210)(174,209)
(175,208)(176,207);;
s2 := (  3,120)(  4,119)(  5,147)(  6,146)(  7,145)(  8,144)(  9,143)( 10,142)
( 11,141)( 12,140)( 13,139)( 14,138)( 15,137)( 16,136)( 17,135)( 18,134)
( 19,133)( 20,132)( 21,131)( 22,130)( 23,129)( 24,128)( 25,127)( 26,126)
( 27,125)( 28,124)( 29,123)( 30,122)( 31,121)( 32,149)( 33,148)( 34,176)
( 35,175)( 36,174)( 37,173)( 38,172)( 39,171)( 40,170)( 41,169)( 42,168)
( 43,167)( 44,166)( 45,165)( 46,164)( 47,163)( 48,162)( 49,161)( 50,160)
( 51,159)( 52,158)( 53,157)( 54,156)( 55,155)( 56,154)( 57,153)( 58,152)
( 59,151)( 60,150)( 61,178)( 62,177)( 63,205)( 64,204)( 65,203)( 66,202)
( 67,201)( 68,200)( 69,199)( 70,198)( 71,197)( 72,196)( 73,195)( 74,194)
( 75,193)( 76,192)( 77,191)( 78,190)( 79,189)( 80,188)( 81,187)( 82,186)
( 83,185)( 84,184)( 85,183)( 86,182)( 87,181)( 88,180)( 89,179)( 90,207)
( 91,206)( 92,234)( 93,233)( 94,232)( 95,231)( 96,230)( 97,229)( 98,228)
( 99,227)(100,226)(101,225)(102,224)(103,223)(104,222)(105,221)(106,220)
(107,219)(108,218)(109,217)(110,216)(111,215)(112,214)(113,213)(114,212)
(115,211)(116,210)(117,209)(118,208);;
s3 := (119,148)(120,149)(121,150)(122,151)(123,152)(124,153)(125,154)(126,155)
(127,156)(128,157)(129,158)(130,159)(131,160)(132,161)(133,162)(134,163)
(135,164)(136,165)(137,166)(138,167)(139,168)(140,169)(141,170)(142,171)
(143,172)(144,173)(145,174)(146,175)(147,176)(177,206)(178,207)(179,208)
(180,209)(181,210)(182,211)(183,212)(184,213)(185,214)(186,215)(187,216)
(188,217)(189,218)(190,219)(191,220)(192,221)(193,222)(194,223)(195,224)
(196,225)(197,226)(198,227)(199,228)(200,229)(201,230)(202,231)(203,232)
(204,233)(205,234);;
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*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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(234)!(1,2);
s1 := Sym(234)!(  4, 31)(  5, 30)(  6, 29)(  7, 28)(  8, 27)(  9, 26)( 10, 25)
( 11, 24)( 12, 23)( 13, 22)( 14, 21)( 15, 20)( 16, 19)( 17, 18)( 33, 60)
( 34, 59)( 35, 58)( 36, 57)( 37, 56)( 38, 55)( 39, 54)( 40, 53)( 41, 52)
( 42, 51)( 43, 50)( 44, 49)( 45, 48)( 46, 47)( 62, 89)( 63, 88)( 64, 87)
( 65, 86)( 66, 85)( 67, 84)( 68, 83)( 69, 82)( 70, 81)( 71, 80)( 72, 79)
( 73, 78)( 74, 77)( 75, 76)( 91,118)( 92,117)( 93,116)( 94,115)( 95,114)
( 96,113)( 97,112)( 98,111)( 99,110)(100,109)(101,108)(102,107)(103,106)
(104,105)(119,177)(120,205)(121,204)(122,203)(123,202)(124,201)(125,200)
(126,199)(127,198)(128,197)(129,196)(130,195)(131,194)(132,193)(133,192)
(134,191)(135,190)(136,189)(137,188)(138,187)(139,186)(140,185)(141,184)
(142,183)(143,182)(144,181)(145,180)(146,179)(147,178)(148,206)(149,234)
(150,233)(151,232)(152,231)(153,230)(154,229)(155,228)(156,227)(157,226)
(158,225)(159,224)(160,223)(161,222)(162,221)(163,220)(164,219)(165,218)
(166,217)(167,216)(168,215)(169,214)(170,213)(171,212)(172,211)(173,210)
(174,209)(175,208)(176,207);
s2 := Sym(234)!(  3,120)(  4,119)(  5,147)(  6,146)(  7,145)(  8,144)(  9,143)
( 10,142)( 11,141)( 12,140)( 13,139)( 14,138)( 15,137)( 16,136)( 17,135)
( 18,134)( 19,133)( 20,132)( 21,131)( 22,130)( 23,129)( 24,128)( 25,127)
( 26,126)( 27,125)( 28,124)( 29,123)( 30,122)( 31,121)( 32,149)( 33,148)
( 34,176)( 35,175)( 36,174)( 37,173)( 38,172)( 39,171)( 40,170)( 41,169)
( 42,168)( 43,167)( 44,166)( 45,165)( 46,164)( 47,163)( 48,162)( 49,161)
( 50,160)( 51,159)( 52,158)( 53,157)( 54,156)( 55,155)( 56,154)( 57,153)
( 58,152)( 59,151)( 60,150)( 61,178)( 62,177)( 63,205)( 64,204)( 65,203)
( 66,202)( 67,201)( 68,200)( 69,199)( 70,198)( 71,197)( 72,196)( 73,195)
( 74,194)( 75,193)( 76,192)( 77,191)( 78,190)( 79,189)( 80,188)( 81,187)
( 82,186)( 83,185)( 84,184)( 85,183)( 86,182)( 87,181)( 88,180)( 89,179)
( 90,207)( 91,206)( 92,234)( 93,233)( 94,232)( 95,231)( 96,230)( 97,229)
( 98,228)( 99,227)(100,226)(101,225)(102,224)(103,223)(104,222)(105,221)
(106,220)(107,219)(108,218)(109,217)(110,216)(111,215)(112,214)(113,213)
(114,212)(115,211)(116,210)(117,209)(118,208);
s3 := Sym(234)!(119,148)(120,149)(121,150)(122,151)(123,152)(124,153)(125,154)
(126,155)(127,156)(128,157)(129,158)(130,159)(131,160)(132,161)(133,162)
(134,163)(135,164)(136,165)(137,166)(138,167)(139,168)(140,169)(141,170)
(142,171)(143,172)(144,173)(145,174)(146,175)(147,176)(177,206)(178,207)
(179,208)(180,209)(181,210)(182,211)(183,212)(184,213)(185,214)(186,215)
(187,216)(188,217)(189,218)(190,219)(191,220)(192,221)(193,222)(194,223)
(195,224)(196,225)(197,226)(198,227)(199,228)(200,229)(201,230)(202,231)
(203,232)(204,233)(205,234);
poly := sub<Sym(234)|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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

to this polytope