Polytope of Type {2,26,18}

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

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