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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*s3*s2*s1*s2*s1*s2*s1*s2*s3*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 ];;
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*s3*s2*s1*s2*s1*s2*s1*s2*s3*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 >; 
 

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