Polytope of Type {2,18,8}

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

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

Permutation Representation (Magma) :

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

to this polytope