Polytope of Type {2,8,18}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,8,18}*1152b
if this polytope has a name.
Group : SmallGroup(1152,155413)
Rank : 4
Schlafli Type : {2,8,18}
Number of vertices, edges, etc : 2, 16, 144, 36
Order of s₀s₁s₂s₃ : 36
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 : {2,8,9}*576, {2,4,18}*576
   3-fold quotients : {2,8,6}*384b
   4-fold quotients : {2,4,9}*288, {2,4,18}*288b, {2,4,18}*288c
   6-fold quotients : {2,8,3}*192, {2,4,6}*192
   8-fold quotients : {2,4,9}*144, {2,2,18}*144
   12-fold quotients : {2,4,3}*96, {2,4,6}*96b, {2,4,6}*96c
   16-fold quotients : {2,2,9}*72
   24-fold quotients : {2,4,3}*48, {2,2,6}*48
   48-fold quotients : {2,2,3}*24
   72-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.

Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (  3, 79)(  4, 80)(  5, 82)(  6, 81)(  7, 76)(  8, 75)(  9, 77)( 10, 78)( 11, 87)( 12, 88)( 13, 90)( 14, 89)( 15, 84)( 16, 83)( 17, 85)( 18, 86)( 19, 95)( 20, 96)( 21, 98)( 22, 97)( 23, 92)( 24, 91)( 25, 93)( 26, 94)( 27,103)( 28,104)( 29,106)( 30,105)( 31,100)( 32, 99)( 33,101)( 34,102)( 35,111)( 36,112)( 37,114)( 38,113)( 39,108)( 40,107)( 41,109)( 42,110)( 43,119)( 44,120)( 45,122)( 46,121)( 47,116)( 48,115)( 49,117)( 50,118)( 51,127)( 52,128)( 53,130)( 54,129)( 55,124)( 56,123)( 57,125)( 58,126)( 59,135)( 60,136)( 61,138)( 62,137)( 63,132)( 64,131)( 65,133)( 66,134)( 67,143)( 68,144)( 69,146)( 70,145)( 71,140)( 72,139)( 73,141)( 74,142)(147,223)(148,224)(149,226)(150,225)(151,220)(152,219)(153,221)(154,222)(155,231)(156,232)(157,234)(158,233)(159,228)(160,227)(161,229)(162,230)(163,239)(164,240)(165,242)(166,241)(167,236)(168,235)(169,237)(170,238)(171,247)(172,248)(173,250)(174,249)(175,244)(176,243)(177,245)(178,246)(179,255)(180,256)(181,258)(182,257)(183,252)(184,251)(185,253)(186,254)(187,263)(188,264)(189,266)(190,265)(191,260)(192,259)(193,261)(194,262)(195,271)(196,272)(197,274)(198,273)(199,268)(200,267)(201,269)(202,270)(203,279)(204,280)(205,282)(206,281)(207,276)(208,275)(209,277)(210,278)(211,287)(212,288)(213,290)(214,289)(215,284)(216,283)(217,285)(218,286);;
s2 := (  5,  8)(  6,  7)(  9, 10)( 11, 19)( 12, 20)( 13, 24)( 14, 23)( 15, 22)( 16, 21)( 17, 26)( 18, 25)( 27, 67)( 28, 68)( 29, 72)( 30, 71)( 31, 70)( 32, 69)( 33, 74)( 34, 73)( 35, 59)( 36, 60)( 37, 64)( 38, 63)( 39, 62)( 40, 61)( 41, 66)( 42, 65)( 43, 51)( 44, 52)( 45, 56)( 46, 55)( 47, 54)( 48, 53)( 49, 58)( 50, 57)( 75, 76)( 77, 79)( 78, 80)( 83, 92)( 84, 91)( 85, 95)( 86, 96)( 87, 93)( 88, 94)( 89, 97)( 90, 98)( 99,140)(100,139)(101,143)(102,144)(103,141)(104,142)(105,145)(106,146)(107,132)(108,131)(109,135)(110,136)(111,133)(112,134)(113,137)(114,138)(115,124)(116,123)(117,127)(118,128)(119,125)(120,126)(121,129)(122,130)(149,152)(150,151)(153,154)(155,163)(156,164)(157,168)(158,167)(159,166)(160,165)(161,170)(162,169)(171,211)(172,212)(173,216)(174,215)(175,214)(176,213)(177,218)(178,217)(179,203)(180,204)(181,208)(182,207)(183,206)(184,205)(185,210)(186,209)(187,195)(188,196)(189,200)(190,199)(191,198)(192,197)(193,202)(194,201)(219,220)(221,223)(222,224)(227,236)(228,235)(229,239)(230,240)(231,237)(232,238)(233,241)(234,242)(243,284)(244,283)(245,287)(246,288)(247,285)(248,286)(249,289)(250,290)(251,276)(252,275)(253,279)(254,280)(255,277)(256,278)(257,281)(258,282)(259,268)(260,267)(261,271)(262,272)(263,269)(264,270)(265,273)(266,274);;
s3 := (  3,195)(  4,196)(  5,201)(  6,202)(  7,200)(  8,199)(  9,197)( 10,198)( 11,211)( 12,212)( 13,217)( 14,218)( 15,216)( 16,215)( 17,213)( 18,214)( 19,203)( 20,204)( 21,209)( 22,210)( 23,208)( 24,207)( 25,205)( 26,206)( 27,171)( 28,172)( 29,177)( 30,178)( 31,176)( 32,175)( 33,173)( 34,174)( 35,187)( 36,188)( 37,193)( 38,194)( 39,192)( 40,191)( 41,189)( 42,190)( 43,179)( 44,180)( 45,185)( 46,186)( 47,184)( 48,183)( 49,181)( 50,182)( 51,147)( 52,148)( 53,153)( 54,154)( 55,152)( 56,151)( 57,149)( 58,150)( 59,163)( 60,164)( 61,169)( 62,170)( 63,168)( 64,167)( 65,165)( 66,166)( 67,155)( 68,156)( 69,161)( 70,162)( 71,160)( 72,159)( 73,157)( 74,158)( 75,268)( 76,267)( 77,274)( 78,273)( 79,271)( 80,272)( 81,270)( 82,269)( 83,284)( 84,283)( 85,290)( 86,289)( 87,287)( 88,288)( 89,286)( 90,285)( 91,276)( 92,275)( 93,282)( 94,281)( 95,279)( 96,280)( 97,278)( 98,277)( 99,244)(100,243)(101,250)(102,249)(103,247)(104,248)(105,246)(106,245)(107,260)(108,259)(109,266)(110,265)(111,263)(112,264)(113,262)(114,261)(115,252)(116,251)(117,258)(118,257)(119,255)(120,256)(121,254)(122,253)(123,220)(124,219)(125,226)(126,225)(127,223)(128,224)(129,222)(130,221)(131,236)(132,235)(133,242)(134,241)(135,239)(136,240)(137,238)(138,237)(139,228)(140,227)(141,234)(142,233)(143,231)(144,232)(145,230)(146,229);;
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*s3*s2*s1*s2*s3*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*s3*s2*s1*s2*s1*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 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(290)!(1,2);
s1 := Sym(290)!(  3, 79)(  4, 80)(  5, 82)(  6, 81)(  7, 76)(  8, 75)(  9, 77)( 10, 78)( 11, 87)( 12, 88)( 13, 90)( 14, 89)( 15, 84)( 16, 83)( 17, 85)( 18, 86)( 19, 95)( 20, 96)( 21, 98)( 22, 97)( 23, 92)( 24, 91)( 25, 93)( 26, 94)( 27,103)( 28,104)( 29,106)( 30,105)( 31,100)( 32, 99)( 33,101)( 34,102)( 35,111)( 36,112)( 37,114)( 38,113)( 39,108)( 40,107)( 41,109)( 42,110)( 43,119)( 44,120)( 45,122)( 46,121)( 47,116)( 48,115)( 49,117)( 50,118)( 51,127)( 52,128)( 53,130)( 54,129)( 55,124)( 56,123)( 57,125)( 58,126)( 59,135)( 60,136)( 61,138)( 62,137)( 63,132)( 64,131)( 65,133)( 66,134)( 67,143)( 68,144)( 69,146)( 70,145)( 71,140)( 72,139)( 73,141)( 74,142)(147,223)(148,224)(149,226)(150,225)(151,220)(152,219)(153,221)(154,222)(155,231)(156,232)(157,234)(158,233)(159,228)(160,227)(161,229)(162,230)(163,239)(164,240)(165,242)(166,241)(167,236)(168,235)(169,237)(170,238)(171,247)(172,248)(173,250)(174,249)(175,244)(176,243)(177,245)(178,246)(179,255)(180,256)(181,258)(182,257)(183,252)(184,251)(185,253)(186,254)(187,263)(188,264)(189,266)(190,265)(191,260)(192,259)(193,261)(194,262)(195,271)(196,272)(197,274)(198,273)(199,268)(200,267)(201,269)(202,270)(203,279)(204,280)(205,282)(206,281)(207,276)(208,275)(209,277)(210,278)(211,287)(212,288)(213,290)(214,289)(215,284)(216,283)(217,285)(218,286);
s2 := Sym(290)!(  5,  8)(  6,  7)(  9, 10)( 11, 19)( 12, 20)( 13, 24)( 14, 23)( 15, 22)( 16, 21)( 17, 26)( 18, 25)( 27, 67)( 28, 68)( 29, 72)( 30, 71)( 31, 70)( 32, 69)( 33, 74)( 34, 73)( 35, 59)( 36, 60)( 37, 64)( 38, 63)( 39, 62)( 40, 61)( 41, 66)( 42, 65)( 43, 51)( 44, 52)( 45, 56)( 46, 55)( 47, 54)( 48, 53)( 49, 58)( 50, 57)( 75, 76)( 77, 79)( 78, 80)( 83, 92)( 84, 91)( 85, 95)( 86, 96)( 87, 93)( 88, 94)( 89, 97)( 90, 98)( 99,140)(100,139)(101,143)(102,144)(103,141)(104,142)(105,145)(106,146)(107,132)(108,131)(109,135)(110,136)(111,133)(112,134)(113,137)(114,138)(115,124)(116,123)(117,127)(118,128)(119,125)(120,126)(121,129)(122,130)(149,152)(150,151)(153,154)(155,163)(156,164)(157,168)(158,167)(159,166)(160,165)(161,170)(162,169)(171,211)(172,212)(173,216)(174,215)(175,214)(176,213)(177,218)(178,217)(179,203)(180,204)(181,208)(182,207)(183,206)(184,205)(185,210)(186,209)(187,195)(188,196)(189,200)(190,199)(191,198)(192,197)(193,202)(194,201)(219,220)(221,223)(222,224)(227,236)(228,235)(229,239)(230,240)(231,237)(232,238)(233,241)(234,242)(243,284)(244,283)(245,287)(246,288)(247,285)(248,286)(249,289)(250,290)(251,276)(252,275)(253,279)(254,280)(255,277)(256,278)(257,281)(258,282)(259,268)(260,267)(261,271)(262,272)(263,269)(264,270)(265,273)(266,274);
s3 := Sym(290)!(  3,195)(  4,196)(  5,201)(  6,202)(  7,200)(  8,199)(  9,197)( 10,198)( 11,211)( 12,212)( 13,217)( 14,218)( 15,216)( 16,215)( 17,213)( 18,214)( 19,203)( 20,204)( 21,209)( 22,210)( 23,208)( 24,207)( 25,205)( 26,206)( 27,171)( 28,172)( 29,177)( 30,178)( 31,176)( 32,175)( 33,173)( 34,174)( 35,187)( 36,188)( 37,193)( 38,194)( 39,192)( 40,191)( 41,189)( 42,190)( 43,179)( 44,180)( 45,185)( 46,186)( 47,184)( 48,183)( 49,181)( 50,182)( 51,147)( 52,148)( 53,153)( 54,154)( 55,152)( 56,151)( 57,149)( 58,150)( 59,163)( 60,164)( 61,169)( 62,170)( 63,168)( 64,167)( 65,165)( 66,166)( 67,155)( 68,156)( 69,161)( 70,162)( 71,160)( 72,159)( 73,157)( 74,158)( 75,268)( 76,267)( 77,274)( 78,273)( 79,271)( 80,272)( 81,270)( 82,269)( 83,284)( 84,283)( 85,290)( 86,289)( 87,287)( 88,288)( 89,286)( 90,285)( 91,276)( 92,275)( 93,282)( 94,281)( 95,279)( 96,280)( 97,278)( 98,277)( 99,244)(100,243)(101,250)(102,249)(103,247)(104,248)(105,246)(106,245)(107,260)(108,259)(109,266)(110,265)(111,263)(112,264)(113,262)(114,261)(115,252)(116,251)(117,258)(118,257)(119,255)(120,256)(121,254)(122,253)(123,220)(124,219)(125,226)(126,225)(127,223)(128,224)(129,222)(130,221)(131,236)(132,235)(133,242)(134,241)(135,239)(136,240)(137,238)(138,237)(139,228)(140,227)(141,234)(142,233)(143,231)(144,232)(145,230)(146,229);
poly := sub<Sym(290)|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*s3*s2*s1*s2*s3*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*s3*s2*s1*s2*s1*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 >;

to this polytope