Polytope of Type {114,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {114,4}*912a
Also Known As : {114,4|2}. if this polytope has another name.
Group : SmallGroup(912,197)
Rank : 3
Schlafli Type : {114,4}
Number of vertices, edges, etc : 114, 228, 4
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 :
   {114,4,2} of size 1824
Vertex Figure Of :
   {2,114,4} of size 1824
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {114,2}*456
   3-fold quotients : {38,4}*304
   4-fold quotients : {57,2}*228
   6-fold quotients : {38,2}*152
   12-fold quotients : {19,2}*76
   19-fold quotients : {6,4}*48a
   38-fold quotients : {6,2}*24
   57-fold quotients : {2,4}*16
   76-fold quotients : {3,2}*12
   114-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {228,4}*1824a, {114,8}*1824
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope