Polytope of Type {2,114,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,114,4}*1824a
if this polytope has a name.
Group : SmallGroup(1824,1228)
Rank : 4
Schlafli Type : {2,114,4}
Number of vertices, edges, etc : 2, 114, 228, 4
Order of s₀s₁s₂s₃ : 228
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 : {2,114,2}*912
   3-fold quotients : {2,38,4}*608
   4-fold quotients : {2,57,2}*456
   6-fold quotients : {2,38,2}*304
   12-fold quotients : {2,19,2}*152
   19-fold quotients : {2,6,4}*96a
   38-fold quotients : {2,6,2}*48
   57-fold quotients : {2,2,4}*32
   76-fold quotients : {2,3,2}*24
   114-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope