Polytope of Type {4,114}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,114}*912a
Also Known As : {4,114|2}. if this polytope has another name.
Group : SmallGroup(912,197)
Rank : 3
Schlafli Type : {4,114}
Number of vertices, edges, etc : 4, 228, 114
Order of s0s1s2 : 228
Order of s0s1s2s1 : 2
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{4,114,2} of size 1824
Vertex Figure Of :
{2,4,114} of size 1824
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2,114}*456
3-fold quotients : {4,38}*304
4-fold quotients : {2,57}*228
6-fold quotients : {2,38}*152
12-fold quotients : {2,19}*76
19-fold quotients : {4,6}*48a
38-fold quotients : {2,6}*24
57-fold quotients : {4,2}*16
76-fold quotients : {2,3}*12
114-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
2-fold covers : {4,228}*1824a, {8,114}*1824
Permutation Representation (GAP) :
s0 := (115,172)(116,173)(117,174)(118,175)(119,176)(120,177)(121,178)(122,179)
(123,180)(124,181)(125,182)(126,183)(127,184)(128,185)(129,186)(130,187)
(131,188)(132,189)(133,190)(134,191)(135,192)(136,193)(137,194)(138,195)
(139,196)(140,197)(141,198)(142,199)(143,200)(144,201)(145,202)(146,203)
(147,204)(148,205)(149,206)(150,207)(151,208)(152,209)(153,210)(154,211)
(155,212)(156,213)(157,214)(158,215)(159,216)(160,217)(161,218)(162,219)
(163,220)(164,221)(165,222)(166,223)(167,224)(168,225)(169,226)(170,227)
(171,228);;
s1 := ( 1,115)( 2,133)( 3,132)( 4,131)( 5,130)( 6,129)( 7,128)( 8,127)
( 9,126)( 10,125)( 11,124)( 12,123)( 13,122)( 14,121)( 15,120)( 16,119)
( 17,118)( 18,117)( 19,116)( 20,153)( 21,171)( 22,170)( 23,169)( 24,168)
( 25,167)( 26,166)( 27,165)( 28,164)( 29,163)( 30,162)( 31,161)( 32,160)
( 33,159)( 34,158)( 35,157)( 36,156)( 37,155)( 38,154)( 39,134)( 40,152)
( 41,151)( 42,150)( 43,149)( 44,148)( 45,147)( 46,146)( 47,145)( 48,144)
( 49,143)( 50,142)( 51,141)( 52,140)( 53,139)( 54,138)( 55,137)( 56,136)
( 57,135)( 58,172)( 59,190)( 60,189)( 61,188)( 62,187)( 63,186)( 64,185)
( 65,184)( 66,183)( 67,182)( 68,181)( 69,180)( 70,179)( 71,178)( 72,177)
( 73,176)( 74,175)( 75,174)( 76,173)( 77,210)( 78,228)( 79,227)( 80,226)
( 81,225)( 82,224)( 83,223)( 84,222)( 85,221)( 86,220)( 87,219)( 88,218)
( 89,217)( 90,216)( 91,215)( 92,214)( 93,213)( 94,212)( 95,211)( 96,191)
( 97,209)( 98,208)( 99,207)(100,206)(101,205)(102,204)(103,203)(104,202)
(105,201)(106,200)(107,199)(108,198)(109,197)(110,196)(111,195)(112,194)
(113,193)(114,192);;
s2 := ( 1, 21)( 2, 20)( 3, 38)( 4, 37)( 5, 36)( 6, 35)( 7, 34)( 8, 33)
( 9, 32)( 10, 31)( 11, 30)( 12, 29)( 13, 28)( 14, 27)( 15, 26)( 16, 25)
( 17, 24)( 18, 23)( 19, 22)( 39, 40)( 41, 57)( 42, 56)( 43, 55)( 44, 54)
( 45, 53)( 46, 52)( 47, 51)( 48, 50)( 58, 78)( 59, 77)( 60, 95)( 61, 94)
( 62, 93)( 63, 92)( 64, 91)( 65, 90)( 66, 89)( 67, 88)( 68, 87)( 69, 86)
( 70, 85)( 71, 84)( 72, 83)( 73, 82)( 74, 81)( 75, 80)( 76, 79)( 96, 97)
( 98,114)( 99,113)(100,112)(101,111)(102,110)(103,109)(104,108)(105,107)
(115,135)(116,134)(117,152)(118,151)(119,150)(120,149)(121,148)(122,147)
(123,146)(124,145)(125,144)(126,143)(127,142)(128,141)(129,140)(130,139)
(131,138)(132,137)(133,136)(153,154)(155,171)(156,170)(157,169)(158,168)
(159,167)(160,166)(161,165)(162,164)(172,192)(173,191)(174,209)(175,208)
(176,207)(177,206)(178,205)(179,204)(180,203)(181,202)(182,201)(183,200)
(184,199)(185,198)(186,197)(187,196)(188,195)(189,194)(190,193)(210,211)
(212,228)(213,227)(214,226)(215,225)(216,224)(217,223)(218,222)(219,221);;
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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(228)!(115,172)(116,173)(117,174)(118,175)(119,176)(120,177)(121,178)
(122,179)(123,180)(124,181)(125,182)(126,183)(127,184)(128,185)(129,186)
(130,187)(131,188)(132,189)(133,190)(134,191)(135,192)(136,193)(137,194)
(138,195)(139,196)(140,197)(141,198)(142,199)(143,200)(144,201)(145,202)
(146,203)(147,204)(148,205)(149,206)(150,207)(151,208)(152,209)(153,210)
(154,211)(155,212)(156,213)(157,214)(158,215)(159,216)(160,217)(161,218)
(162,219)(163,220)(164,221)(165,222)(166,223)(167,224)(168,225)(169,226)
(170,227)(171,228);
s1 := Sym(228)!( 1,115)( 2,133)( 3,132)( 4,131)( 5,130)( 6,129)( 7,128)
( 8,127)( 9,126)( 10,125)( 11,124)( 12,123)( 13,122)( 14,121)( 15,120)
( 16,119)( 17,118)( 18,117)( 19,116)( 20,153)( 21,171)( 22,170)( 23,169)
( 24,168)( 25,167)( 26,166)( 27,165)( 28,164)( 29,163)( 30,162)( 31,161)
( 32,160)( 33,159)( 34,158)( 35,157)( 36,156)( 37,155)( 38,154)( 39,134)
( 40,152)( 41,151)( 42,150)( 43,149)( 44,148)( 45,147)( 46,146)( 47,145)
( 48,144)( 49,143)( 50,142)( 51,141)( 52,140)( 53,139)( 54,138)( 55,137)
( 56,136)( 57,135)( 58,172)( 59,190)( 60,189)( 61,188)( 62,187)( 63,186)
( 64,185)( 65,184)( 66,183)( 67,182)( 68,181)( 69,180)( 70,179)( 71,178)
( 72,177)( 73,176)( 74,175)( 75,174)( 76,173)( 77,210)( 78,228)( 79,227)
( 80,226)( 81,225)( 82,224)( 83,223)( 84,222)( 85,221)( 86,220)( 87,219)
( 88,218)( 89,217)( 90,216)( 91,215)( 92,214)( 93,213)( 94,212)( 95,211)
( 96,191)( 97,209)( 98,208)( 99,207)(100,206)(101,205)(102,204)(103,203)
(104,202)(105,201)(106,200)(107,199)(108,198)(109,197)(110,196)(111,195)
(112,194)(113,193)(114,192);
s2 := Sym(228)!( 1, 21)( 2, 20)( 3, 38)( 4, 37)( 5, 36)( 6, 35)( 7, 34)
( 8, 33)( 9, 32)( 10, 31)( 11, 30)( 12, 29)( 13, 28)( 14, 27)( 15, 26)
( 16, 25)( 17, 24)( 18, 23)( 19, 22)( 39, 40)( 41, 57)( 42, 56)( 43, 55)
( 44, 54)( 45, 53)( 46, 52)( 47, 51)( 48, 50)( 58, 78)( 59, 77)( 60, 95)
( 61, 94)( 62, 93)( 63, 92)( 64, 91)( 65, 90)( 66, 89)( 67, 88)( 68, 87)
( 69, 86)( 70, 85)( 71, 84)( 72, 83)( 73, 82)( 74, 81)( 75, 80)( 76, 79)
( 96, 97)( 98,114)( 99,113)(100,112)(101,111)(102,110)(103,109)(104,108)
(105,107)(115,135)(116,134)(117,152)(118,151)(119,150)(120,149)(121,148)
(122,147)(123,146)(124,145)(125,144)(126,143)(127,142)(128,141)(129,140)
(130,139)(131,138)(132,137)(133,136)(153,154)(155,171)(156,170)(157,169)
(158,168)(159,167)(160,166)(161,165)(162,164)(172,192)(173,191)(174,209)
(175,208)(176,207)(177,206)(178,205)(179,204)(180,203)(181,202)(182,201)
(183,200)(184,199)(185,198)(186,197)(187,196)(188,195)(189,194)(190,193)
(210,211)(212,228)(213,227)(214,226)(215,225)(216,224)(217,223)(218,222)
(219,221);
poly := sub<Sym(228)|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 >;
References : None.
to this polytope