Polytope of Type {26,18}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {26,18}*936
Also Known As : {26,18|2}. if this polytope has another name.
Group : SmallGroup(936,64)
Rank : 3
Schlafli Type : {26,18}
Number of vertices, edges, etc : 26, 234, 18
Order of s₀s₁s₂ : 234
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {26,18,2} of size 1872
Vertex Figure Of :
   {2,26,18} of size 1872
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {26,6}*312
   9-fold quotients : {26,2}*104
   13-fold quotients : {2,18}*72
   18-fold quotients : {13,2}*52
   26-fold quotients : {2,9}*36
   39-fold quotients : {2,6}*24
   78-fold quotients : {2,3}*12
   117-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {26,36}*1872, {52,18}*1872a
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope