Polytope of Type {18,8,2}

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

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

Permutation Representation (Magma) :

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

to this polytope