Polytope of Type {4,116}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,116}*928
Also Known As : {4,116|2}. if this polytope has another name.
Group : SmallGroup(928,103)
Rank : 3
Schlafli Type : {4,116}
Number of vertices, edges, etc : 4, 232, 116
Order of s0s1s2 : 116
Order of s0s1s2s1 : 2
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{4,116,2} of size 1856
Vertex Figure Of :
{2,4,116} of size 1856
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2,116}*464, {4,58}*464
4-fold quotients : {2,58}*232
8-fold quotients : {2,29}*116
29-fold quotients : {4,4}*32
58-fold quotients : {2,4}*16, {4,2}*16
116-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
2-fold covers : {8,116}*1856a, {4,232}*1856a, {8,116}*1856b, {4,232}*1856b, {4,116}*1856
Permutation Representation (GAP) :
s0 := (117,146)(118,147)(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)(175,204)(176,205)(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);;
s1 := ( 1,117)( 2,145)( 3,144)( 4,143)( 5,142)( 6,141)( 7,140)( 8,139)
( 9,138)( 10,137)( 11,136)( 12,135)( 13,134)( 14,133)( 15,132)( 16,131)
( 17,130)( 18,129)( 19,128)( 20,127)( 21,126)( 22,125)( 23,124)( 24,123)
( 25,122)( 26,121)( 27,120)( 28,119)( 29,118)( 30,146)( 31,174)( 32,173)
( 33,172)( 34,171)( 35,170)( 36,169)( 37,168)( 38,167)( 39,166)( 40,165)
( 41,164)( 42,163)( 43,162)( 44,161)( 45,160)( 46,159)( 47,158)( 48,157)
( 49,156)( 50,155)( 51,154)( 52,153)( 53,152)( 54,151)( 55,150)( 56,149)
( 57,148)( 58,147)( 59,175)( 60,203)( 61,202)( 62,201)( 63,200)( 64,199)
( 65,198)( 66,197)( 67,196)( 68,195)( 69,194)( 70,193)( 71,192)( 72,191)
( 73,190)( 74,189)( 75,188)( 76,187)( 77,186)( 78,185)( 79,184)( 80,183)
( 81,182)( 82,181)( 83,180)( 84,179)( 85,178)( 86,177)( 87,176)( 88,204)
( 89,232)( 90,231)( 91,230)( 92,229)( 93,228)( 94,227)( 95,226)( 96,225)
( 97,224)( 98,223)( 99,222)(100,221)(101,220)(102,219)(103,218)(104,217)
(105,216)(106,215)(107,214)(108,213)(109,212)(110,211)(111,210)(112,209)
(113,208)(114,207)(115,206)(116,205);;
s2 := ( 1, 2)( 3, 29)( 4, 28)( 5, 27)( 6, 26)( 7, 25)( 8, 24)( 9, 23)
( 10, 22)( 11, 21)( 12, 20)( 13, 19)( 14, 18)( 15, 17)( 30, 31)( 32, 58)
( 33, 57)( 34, 56)( 35, 55)( 36, 54)( 37, 53)( 38, 52)( 39, 51)( 40, 50)
( 41, 49)( 42, 48)( 43, 47)( 44, 46)( 59, 60)( 61, 87)( 62, 86)( 63, 85)
( 64, 84)( 65, 83)( 66, 82)( 67, 81)( 68, 80)( 69, 79)( 70, 78)( 71, 77)
( 72, 76)( 73, 75)( 88, 89)( 90,116)( 91,115)( 92,114)( 93,113)( 94,112)
( 95,111)( 96,110)( 97,109)( 98,108)( 99,107)(100,106)(101,105)(102,104)
(117,176)(118,175)(119,203)(120,202)(121,201)(122,200)(123,199)(124,198)
(125,197)(126,196)(127,195)(128,194)(129,193)(130,192)(131,191)(132,190)
(133,189)(134,188)(135,187)(136,186)(137,185)(138,184)(139,183)(140,182)
(141,181)(142,180)(143,179)(144,178)(145,177)(146,205)(147,204)(148,232)
(149,231)(150,230)(151,229)(152,228)(153,227)(154,226)(155,225)(156,224)
(157,223)(158,222)(159,221)(160,220)(161,219)(162,218)(163,217)(164,216)
(165,215)(166,214)(167,213)(168,212)(169,211)(170,210)(171,209)(172,208)
(173,207)(174,206);;
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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(232)!(117,146)(118,147)(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)(175,204)(176,205)
(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);
s1 := Sym(232)!( 1,117)( 2,145)( 3,144)( 4,143)( 5,142)( 6,141)( 7,140)
( 8,139)( 9,138)( 10,137)( 11,136)( 12,135)( 13,134)( 14,133)( 15,132)
( 16,131)( 17,130)( 18,129)( 19,128)( 20,127)( 21,126)( 22,125)( 23,124)
( 24,123)( 25,122)( 26,121)( 27,120)( 28,119)( 29,118)( 30,146)( 31,174)
( 32,173)( 33,172)( 34,171)( 35,170)( 36,169)( 37,168)( 38,167)( 39,166)
( 40,165)( 41,164)( 42,163)( 43,162)( 44,161)( 45,160)( 46,159)( 47,158)
( 48,157)( 49,156)( 50,155)( 51,154)( 52,153)( 53,152)( 54,151)( 55,150)
( 56,149)( 57,148)( 58,147)( 59,175)( 60,203)( 61,202)( 62,201)( 63,200)
( 64,199)( 65,198)( 66,197)( 67,196)( 68,195)( 69,194)( 70,193)( 71,192)
( 72,191)( 73,190)( 74,189)( 75,188)( 76,187)( 77,186)( 78,185)( 79,184)
( 80,183)( 81,182)( 82,181)( 83,180)( 84,179)( 85,178)( 86,177)( 87,176)
( 88,204)( 89,232)( 90,231)( 91,230)( 92,229)( 93,228)( 94,227)( 95,226)
( 96,225)( 97,224)( 98,223)( 99,222)(100,221)(101,220)(102,219)(103,218)
(104,217)(105,216)(106,215)(107,214)(108,213)(109,212)(110,211)(111,210)
(112,209)(113,208)(114,207)(115,206)(116,205);
s2 := Sym(232)!( 1, 2)( 3, 29)( 4, 28)( 5, 27)( 6, 26)( 7, 25)( 8, 24)
( 9, 23)( 10, 22)( 11, 21)( 12, 20)( 13, 19)( 14, 18)( 15, 17)( 30, 31)
( 32, 58)( 33, 57)( 34, 56)( 35, 55)( 36, 54)( 37, 53)( 38, 52)( 39, 51)
( 40, 50)( 41, 49)( 42, 48)( 43, 47)( 44, 46)( 59, 60)( 61, 87)( 62, 86)
( 63, 85)( 64, 84)( 65, 83)( 66, 82)( 67, 81)( 68, 80)( 69, 79)( 70, 78)
( 71, 77)( 72, 76)( 73, 75)( 88, 89)( 90,116)( 91,115)( 92,114)( 93,113)
( 94,112)( 95,111)( 96,110)( 97,109)( 98,108)( 99,107)(100,106)(101,105)
(102,104)(117,176)(118,175)(119,203)(120,202)(121,201)(122,200)(123,199)
(124,198)(125,197)(126,196)(127,195)(128,194)(129,193)(130,192)(131,191)
(132,190)(133,189)(134,188)(135,187)(136,186)(137,185)(138,184)(139,183)
(140,182)(141,181)(142,180)(143,179)(144,178)(145,177)(146,205)(147,204)
(148,232)(149,231)(150,230)(151,229)(152,228)(153,227)(154,226)(155,225)
(156,224)(157,223)(158,222)(159,221)(160,220)(161,219)(162,218)(163,217)
(164,216)(165,215)(166,214)(167,213)(168,212)(169,211)(170,210)(171,209)
(172,208)(173,207)(174,206);
poly := sub<Sym(232)|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 >;
References : None.
to this polytope