Polytope of Type {2,18,26}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,18,26}*1872
if this polytope has a name.
Group : SmallGroup(1872,548)
Rank : 4
Schlafli Type : {2,18,26}
Number of vertices, edges, etc : 2, 18, 234, 26
Order of s₀s₁s₂s₃ : 234
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) :
   3-fold quotients : {2,6,26}*624
   9-fold quotients : {2,2,26}*208
   13-fold quotients : {2,18,2}*144
   18-fold quotients : {2,2,13}*104
   26-fold quotients : {2,9,2}*72
   39-fold quotients : {2,6,2}*48
   78-fold quotients : {2,3,2}*24
   117-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (  4,  5)(  7,  8)( 10, 11)( 13, 14)( 16, 17)( 19, 20)( 22, 23)( 25, 26)
( 28, 29)( 31, 32)( 34, 35)( 37, 38)( 40, 41)( 42, 83)( 43, 82)( 44, 81)
( 45, 86)( 46, 85)( 47, 84)( 48, 89)( 49, 88)( 50, 87)( 51, 92)( 52, 91)
( 53, 90)( 54, 95)( 55, 94)( 56, 93)( 57, 98)( 58, 97)( 59, 96)( 60,101)
( 61,100)( 62, 99)( 63,104)( 64,103)( 65,102)( 66,107)( 67,106)( 68,105)
( 69,110)( 70,109)( 71,108)( 72,113)( 73,112)( 74,111)( 75,116)( 76,115)
( 77,114)( 78,119)( 79,118)( 80,117)(121,122)(124,125)(127,128)(130,131)
(133,134)(136,137)(139,140)(142,143)(145,146)(148,149)(151,152)(154,155)
(157,158)(159,200)(160,199)(161,198)(162,203)(163,202)(164,201)(165,206)
(166,205)(167,204)(168,209)(169,208)(170,207)(171,212)(172,211)(173,210)
(174,215)(175,214)(176,213)(177,218)(178,217)(179,216)(180,221)(181,220)
(182,219)(183,224)(184,223)(185,222)(186,227)(187,226)(188,225)(189,230)
(190,229)(191,228)(192,233)(193,232)(194,231)(195,236)(196,235)(197,234);;
s2 := (  3, 42)(  4, 44)(  5, 43)(  6, 78)(  7, 80)(  8, 79)(  9, 75)( 10, 77)
( 11, 76)( 12, 72)( 13, 74)( 14, 73)( 15, 69)( 16, 71)( 17, 70)( 18, 66)
( 19, 68)( 20, 67)( 21, 63)( 22, 65)( 23, 64)( 24, 60)( 25, 62)( 26, 61)
( 27, 57)( 28, 59)( 29, 58)( 30, 54)( 31, 56)( 32, 55)( 33, 51)( 34, 53)
( 35, 52)( 36, 48)( 37, 50)( 38, 49)( 39, 45)( 40, 47)( 41, 46)( 81, 83)
( 84,119)( 85,118)( 86,117)( 87,116)( 88,115)( 89,114)( 90,113)( 91,112)
( 92,111)( 93,110)( 94,109)( 95,108)( 96,107)( 97,106)( 98,105)( 99,104)
(100,103)(101,102)(120,159)(121,161)(122,160)(123,195)(124,197)(125,196)
(126,192)(127,194)(128,193)(129,189)(130,191)(131,190)(132,186)(133,188)
(134,187)(135,183)(136,185)(137,184)(138,180)(139,182)(140,181)(141,177)
(142,179)(143,178)(144,174)(145,176)(146,175)(147,171)(148,173)(149,172)
(150,168)(151,170)(152,169)(153,165)(154,167)(155,166)(156,162)(157,164)
(158,163)(198,200)(201,236)(202,235)(203,234)(204,233)(205,232)(206,231)
(207,230)(208,229)(209,228)(210,227)(211,226)(212,225)(213,224)(214,223)
(215,222)(216,221)(217,220)(218,219);;
s3 := (  3,123)(  4,124)(  5,125)(  6,120)(  7,121)(  8,122)(  9,156)( 10,157)
( 11,158)( 12,153)( 13,154)( 14,155)( 15,150)( 16,151)( 17,152)( 18,147)
( 19,148)( 20,149)( 21,144)( 22,145)( 23,146)( 24,141)( 25,142)( 26,143)
( 27,138)( 28,139)( 29,140)( 30,135)( 31,136)( 32,137)( 33,132)( 34,133)
( 35,134)( 36,129)( 37,130)( 38,131)( 39,126)( 40,127)( 41,128)( 42,162)
( 43,163)( 44,164)( 45,159)( 46,160)( 47,161)( 48,195)( 49,196)( 50,197)
( 51,192)( 52,193)( 53,194)( 54,189)( 55,190)( 56,191)( 57,186)( 58,187)
( 59,188)( 60,183)( 61,184)( 62,185)( 63,180)( 64,181)( 65,182)( 66,177)
( 67,178)( 68,179)( 69,174)( 70,175)( 71,176)( 72,171)( 73,172)( 74,173)
( 75,168)( 76,169)( 77,170)( 78,165)( 79,166)( 80,167)( 81,201)( 82,202)
( 83,203)( 84,198)( 85,199)( 86,200)( 87,234)( 88,235)( 89,236)( 90,231)
( 91,232)( 92,233)( 93,228)( 94,229)( 95,230)( 96,225)( 97,226)( 98,227)
( 99,222)(100,223)(101,224)(102,219)(103,220)(104,221)(105,216)(106,217)
(107,218)(108,213)(109,214)(110,215)(111,210)(112,211)(113,212)(114,207)
(115,208)(116,209)(117,204)(118,205)(119,206);;
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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(236)!(1,2);
s1 := Sym(236)!(  4,  5)(  7,  8)( 10, 11)( 13, 14)( 16, 17)( 19, 20)( 22, 23)
( 25, 26)( 28, 29)( 31, 32)( 34, 35)( 37, 38)( 40, 41)( 42, 83)( 43, 82)
( 44, 81)( 45, 86)( 46, 85)( 47, 84)( 48, 89)( 49, 88)( 50, 87)( 51, 92)
( 52, 91)( 53, 90)( 54, 95)( 55, 94)( 56, 93)( 57, 98)( 58, 97)( 59, 96)
( 60,101)( 61,100)( 62, 99)( 63,104)( 64,103)( 65,102)( 66,107)( 67,106)
( 68,105)( 69,110)( 70,109)( 71,108)( 72,113)( 73,112)( 74,111)( 75,116)
( 76,115)( 77,114)( 78,119)( 79,118)( 80,117)(121,122)(124,125)(127,128)
(130,131)(133,134)(136,137)(139,140)(142,143)(145,146)(148,149)(151,152)
(154,155)(157,158)(159,200)(160,199)(161,198)(162,203)(163,202)(164,201)
(165,206)(166,205)(167,204)(168,209)(169,208)(170,207)(171,212)(172,211)
(173,210)(174,215)(175,214)(176,213)(177,218)(178,217)(179,216)(180,221)
(181,220)(182,219)(183,224)(184,223)(185,222)(186,227)(187,226)(188,225)
(189,230)(190,229)(191,228)(192,233)(193,232)(194,231)(195,236)(196,235)
(197,234);
s2 := Sym(236)!(  3, 42)(  4, 44)(  5, 43)(  6, 78)(  7, 80)(  8, 79)(  9, 75)
( 10, 77)( 11, 76)( 12, 72)( 13, 74)( 14, 73)( 15, 69)( 16, 71)( 17, 70)
( 18, 66)( 19, 68)( 20, 67)( 21, 63)( 22, 65)( 23, 64)( 24, 60)( 25, 62)
( 26, 61)( 27, 57)( 28, 59)( 29, 58)( 30, 54)( 31, 56)( 32, 55)( 33, 51)
( 34, 53)( 35, 52)( 36, 48)( 37, 50)( 38, 49)( 39, 45)( 40, 47)( 41, 46)
( 81, 83)( 84,119)( 85,118)( 86,117)( 87,116)( 88,115)( 89,114)( 90,113)
( 91,112)( 92,111)( 93,110)( 94,109)( 95,108)( 96,107)( 97,106)( 98,105)
( 99,104)(100,103)(101,102)(120,159)(121,161)(122,160)(123,195)(124,197)
(125,196)(126,192)(127,194)(128,193)(129,189)(130,191)(131,190)(132,186)
(133,188)(134,187)(135,183)(136,185)(137,184)(138,180)(139,182)(140,181)
(141,177)(142,179)(143,178)(144,174)(145,176)(146,175)(147,171)(148,173)
(149,172)(150,168)(151,170)(152,169)(153,165)(154,167)(155,166)(156,162)
(157,164)(158,163)(198,200)(201,236)(202,235)(203,234)(204,233)(205,232)
(206,231)(207,230)(208,229)(209,228)(210,227)(211,226)(212,225)(213,224)
(214,223)(215,222)(216,221)(217,220)(218,219);
s3 := Sym(236)!(  3,123)(  4,124)(  5,125)(  6,120)(  7,121)(  8,122)(  9,156)
( 10,157)( 11,158)( 12,153)( 13,154)( 14,155)( 15,150)( 16,151)( 17,152)
( 18,147)( 19,148)( 20,149)( 21,144)( 22,145)( 23,146)( 24,141)( 25,142)
( 26,143)( 27,138)( 28,139)( 29,140)( 30,135)( 31,136)( 32,137)( 33,132)
( 34,133)( 35,134)( 36,129)( 37,130)( 38,131)( 39,126)( 40,127)( 41,128)
( 42,162)( 43,163)( 44,164)( 45,159)( 46,160)( 47,161)( 48,195)( 49,196)
( 50,197)( 51,192)( 52,193)( 53,194)( 54,189)( 55,190)( 56,191)( 57,186)
( 58,187)( 59,188)( 60,183)( 61,184)( 62,185)( 63,180)( 64,181)( 65,182)
( 66,177)( 67,178)( 68,179)( 69,174)( 70,175)( 71,176)( 72,171)( 73,172)
( 74,173)( 75,168)( 76,169)( 77,170)( 78,165)( 79,166)( 80,167)( 81,201)
( 82,202)( 83,203)( 84,198)( 85,199)( 86,200)( 87,234)( 88,235)( 89,236)
( 90,231)( 91,232)( 92,233)( 93,228)( 94,229)( 95,230)( 96,225)( 97,226)
( 98,227)( 99,222)(100,223)(101,224)(102,219)(103,220)(104,221)(105,216)
(106,217)(107,218)(108,213)(109,214)(110,215)(111,210)(112,211)(113,212)
(114,207)(115,208)(116,209)(117,204)(118,205)(119,206);
poly := sub<Sym(236)|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, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

to this polytope