Polytope of Type {4,18,4,2}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,18,4,2}*1152d
if this polytope has a name.
Group : SmallGroup(1152,157449)
Rank : 5
Schlafli Type : {4,18,4,2}
Number of vertices, edges, etc : 4, 36, 36, 4, 2
Order of s0s1s2s3s4 : 18
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Non-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 : {4,9,4,2}*576
3-fold quotients : {4,6,4,2}*384d
6-fold quotients : {4,3,4,2}*192
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1, 9)( 2, 10)( 3, 11)( 4, 12)( 5, 13)( 6, 14)( 7, 15)( 8, 16)
( 17, 25)( 18, 26)( 19, 27)( 20, 28)( 21, 29)( 22, 30)( 23, 31)( 24, 32)
( 33, 41)( 34, 42)( 35, 43)( 36, 44)( 37, 45)( 38, 46)( 39, 47)( 40, 48)
( 49, 57)( 50, 58)( 51, 59)( 52, 60)( 53, 61)( 54, 62)( 55, 63)( 56, 64)
( 65, 73)( 66, 74)( 67, 75)( 68, 76)( 69, 77)( 70, 78)( 71, 79)( 72, 80)
( 81, 89)( 82, 90)( 83, 91)( 84, 92)( 85, 93)( 86, 94)( 87, 95)( 88, 96)
( 97,105)( 98,106)( 99,107)(100,108)(101,109)(102,110)(103,111)(104,112)
(113,121)(114,122)(115,123)(116,124)(117,125)(118,126)(119,127)(120,128)
(129,137)(130,138)(131,139)(132,140)(133,141)(134,142)(135,143)(136,144)
(145,153)(146,154)(147,155)(148,156)(149,157)(150,158)(151,159)(152,160)
(161,169)(162,170)(163,171)(164,172)(165,173)(166,174)(167,175)(168,176)
(177,185)(178,186)(179,187)(180,188)(181,189)(182,190)(183,191)(184,192)
(193,201)(194,202)(195,203)(196,204)(197,205)(198,206)(199,207)(200,208)
(209,217)(210,218)(211,219)(212,220)(213,221)(214,222)(215,223)(216,224)
(225,233)(226,234)(227,235)(228,236)(229,237)(230,238)(231,239)(232,240)
(241,249)(242,250)(243,251)(244,252)(245,253)(246,254)(247,255)(248,256)
(257,265)(258,266)(259,267)(260,268)(261,269)(262,270)(263,271)(264,272)
(273,281)(274,282)(275,283)(276,284)(277,285)(278,286)(279,287)(280,288);;
s1 := ( 1, 49)( 2, 52)( 3, 51)( 4, 50)( 5, 57)( 6, 60)( 7, 59)( 8, 58)
( 9, 53)( 10, 56)( 11, 55)( 12, 54)( 13, 61)( 14, 64)( 15, 63)( 16, 62)
( 17, 81)( 18, 84)( 19, 83)( 20, 82)( 21, 89)( 22, 92)( 23, 91)( 24, 90)
( 25, 85)( 26, 88)( 27, 87)( 28, 86)( 29, 93)( 30, 96)( 31, 95)( 32, 94)
( 33, 65)( 34, 68)( 35, 67)( 36, 66)( 37, 73)( 38, 76)( 39, 75)( 40, 74)
( 41, 69)( 42, 72)( 43, 71)( 44, 70)( 45, 77)( 46, 80)( 47, 79)( 48, 78)
( 97,113)( 98,116)( 99,115)(100,114)(101,121)(102,124)(103,123)(104,122)
(105,117)(106,120)(107,119)(108,118)(109,125)(110,128)(111,127)(112,126)
(130,132)(133,137)(134,140)(135,139)(136,138)(142,144)(145,193)(146,196)
(147,195)(148,194)(149,201)(150,204)(151,203)(152,202)(153,197)(154,200)
(155,199)(156,198)(157,205)(158,208)(159,207)(160,206)(161,225)(162,228)
(163,227)(164,226)(165,233)(166,236)(167,235)(168,234)(169,229)(170,232)
(171,231)(172,230)(173,237)(174,240)(175,239)(176,238)(177,209)(178,212)
(179,211)(180,210)(181,217)(182,220)(183,219)(184,218)(185,213)(186,216)
(187,215)(188,214)(189,221)(190,224)(191,223)(192,222)(241,257)(242,260)
(243,259)(244,258)(245,265)(246,268)(247,267)(248,266)(249,261)(250,264)
(251,263)(252,262)(253,269)(254,272)(255,271)(256,270)(274,276)(277,281)
(278,284)(279,283)(280,282)(286,288);;
s2 := ( 1,145)( 2,146)( 3,148)( 4,147)( 5,157)( 6,158)( 7,160)( 8,159)
( 9,153)( 10,154)( 11,156)( 12,155)( 13,149)( 14,150)( 15,152)( 16,151)
( 17,177)( 18,178)( 19,180)( 20,179)( 21,189)( 22,190)( 23,192)( 24,191)
( 25,185)( 26,186)( 27,188)( 28,187)( 29,181)( 30,182)( 31,184)( 32,183)
( 33,161)( 34,162)( 35,164)( 36,163)( 37,173)( 38,174)( 39,176)( 40,175)
( 41,169)( 42,170)( 43,172)( 44,171)( 45,165)( 46,166)( 47,168)( 48,167)
( 49,257)( 50,258)( 51,260)( 52,259)( 53,269)( 54,270)( 55,272)( 56,271)
( 57,265)( 58,266)( 59,268)( 60,267)( 61,261)( 62,262)( 63,264)( 64,263)
( 65,241)( 66,242)( 67,244)( 68,243)( 69,253)( 70,254)( 71,256)( 72,255)
( 73,249)( 74,250)( 75,252)( 76,251)( 77,245)( 78,246)( 79,248)( 80,247)
( 81,273)( 82,274)( 83,276)( 84,275)( 85,285)( 86,286)( 87,288)( 88,287)
( 89,281)( 90,282)( 91,284)( 92,283)( 93,277)( 94,278)( 95,280)( 96,279)
( 97,209)( 98,210)( 99,212)(100,211)(101,221)(102,222)(103,224)(104,223)
(105,217)(106,218)(107,220)(108,219)(109,213)(110,214)(111,216)(112,215)
(113,193)(114,194)(115,196)(116,195)(117,205)(118,206)(119,208)(120,207)
(121,201)(122,202)(123,204)(124,203)(125,197)(126,198)(127,200)(128,199)
(129,225)(130,226)(131,228)(132,227)(133,237)(134,238)(135,240)(136,239)
(137,233)(138,234)(139,236)(140,235)(141,229)(142,230)(143,232)(144,231);;
s3 := ( 1, 3)( 2, 4)( 5, 7)( 6, 8)( 9, 11)( 10, 12)( 13, 15)( 14, 16)
( 17, 19)( 18, 20)( 21, 23)( 22, 24)( 25, 27)( 26, 28)( 29, 31)( 30, 32)
( 33, 35)( 34, 36)( 37, 39)( 38, 40)( 41, 43)( 42, 44)( 45, 47)( 46, 48)
( 49, 51)( 50, 52)( 53, 55)( 54, 56)( 57, 59)( 58, 60)( 61, 63)( 62, 64)
( 65, 67)( 66, 68)( 69, 71)( 70, 72)( 73, 75)( 74, 76)( 77, 79)( 78, 80)
( 81, 83)( 82, 84)( 85, 87)( 86, 88)( 89, 91)( 90, 92)( 93, 95)( 94, 96)
( 97, 99)( 98,100)(101,103)(102,104)(105,107)(106,108)(109,111)(110,112)
(113,115)(114,116)(117,119)(118,120)(121,123)(122,124)(125,127)(126,128)
(129,131)(130,132)(133,135)(134,136)(137,139)(138,140)(141,143)(142,144)
(145,147)(146,148)(149,151)(150,152)(153,155)(154,156)(157,159)(158,160)
(161,163)(162,164)(165,167)(166,168)(169,171)(170,172)(173,175)(174,176)
(177,179)(178,180)(181,183)(182,184)(185,187)(186,188)(189,191)(190,192)
(193,195)(194,196)(197,199)(198,200)(201,203)(202,204)(205,207)(206,208)
(209,211)(210,212)(213,215)(214,216)(217,219)(218,220)(221,223)(222,224)
(225,227)(226,228)(229,231)(230,232)(233,235)(234,236)(237,239)(238,240)
(241,243)(242,244)(245,247)(246,248)(249,251)(250,252)(253,255)(254,256)
(257,259)(258,260)(261,263)(262,264)(265,267)(266,268)(269,271)(270,272)
(273,275)(274,276)(277,279)(278,280)(281,283)(282,284)(285,287)(286,288);;
s4 := (289,290);;
poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4,
s0*s1*s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3,
s0*s1*s2*s1*s0*s1*s2*s0*s1, s3*s2*s1*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*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, 9)( 2, 10)( 3, 11)( 4, 12)( 5, 13)( 6, 14)( 7, 15)
( 8, 16)( 17, 25)( 18, 26)( 19, 27)( 20, 28)( 21, 29)( 22, 30)( 23, 31)
( 24, 32)( 33, 41)( 34, 42)( 35, 43)( 36, 44)( 37, 45)( 38, 46)( 39, 47)
( 40, 48)( 49, 57)( 50, 58)( 51, 59)( 52, 60)( 53, 61)( 54, 62)( 55, 63)
( 56, 64)( 65, 73)( 66, 74)( 67, 75)( 68, 76)( 69, 77)( 70, 78)( 71, 79)
( 72, 80)( 81, 89)( 82, 90)( 83, 91)( 84, 92)( 85, 93)( 86, 94)( 87, 95)
( 88, 96)( 97,105)( 98,106)( 99,107)(100,108)(101,109)(102,110)(103,111)
(104,112)(113,121)(114,122)(115,123)(116,124)(117,125)(118,126)(119,127)
(120,128)(129,137)(130,138)(131,139)(132,140)(133,141)(134,142)(135,143)
(136,144)(145,153)(146,154)(147,155)(148,156)(149,157)(150,158)(151,159)
(152,160)(161,169)(162,170)(163,171)(164,172)(165,173)(166,174)(167,175)
(168,176)(177,185)(178,186)(179,187)(180,188)(181,189)(182,190)(183,191)
(184,192)(193,201)(194,202)(195,203)(196,204)(197,205)(198,206)(199,207)
(200,208)(209,217)(210,218)(211,219)(212,220)(213,221)(214,222)(215,223)
(216,224)(225,233)(226,234)(227,235)(228,236)(229,237)(230,238)(231,239)
(232,240)(241,249)(242,250)(243,251)(244,252)(245,253)(246,254)(247,255)
(248,256)(257,265)(258,266)(259,267)(260,268)(261,269)(262,270)(263,271)
(264,272)(273,281)(274,282)(275,283)(276,284)(277,285)(278,286)(279,287)
(280,288);
s1 := Sym(290)!( 1, 49)( 2, 52)( 3, 51)( 4, 50)( 5, 57)( 6, 60)( 7, 59)
( 8, 58)( 9, 53)( 10, 56)( 11, 55)( 12, 54)( 13, 61)( 14, 64)( 15, 63)
( 16, 62)( 17, 81)( 18, 84)( 19, 83)( 20, 82)( 21, 89)( 22, 92)( 23, 91)
( 24, 90)( 25, 85)( 26, 88)( 27, 87)( 28, 86)( 29, 93)( 30, 96)( 31, 95)
( 32, 94)( 33, 65)( 34, 68)( 35, 67)( 36, 66)( 37, 73)( 38, 76)( 39, 75)
( 40, 74)( 41, 69)( 42, 72)( 43, 71)( 44, 70)( 45, 77)( 46, 80)( 47, 79)
( 48, 78)( 97,113)( 98,116)( 99,115)(100,114)(101,121)(102,124)(103,123)
(104,122)(105,117)(106,120)(107,119)(108,118)(109,125)(110,128)(111,127)
(112,126)(130,132)(133,137)(134,140)(135,139)(136,138)(142,144)(145,193)
(146,196)(147,195)(148,194)(149,201)(150,204)(151,203)(152,202)(153,197)
(154,200)(155,199)(156,198)(157,205)(158,208)(159,207)(160,206)(161,225)
(162,228)(163,227)(164,226)(165,233)(166,236)(167,235)(168,234)(169,229)
(170,232)(171,231)(172,230)(173,237)(174,240)(175,239)(176,238)(177,209)
(178,212)(179,211)(180,210)(181,217)(182,220)(183,219)(184,218)(185,213)
(186,216)(187,215)(188,214)(189,221)(190,224)(191,223)(192,222)(241,257)
(242,260)(243,259)(244,258)(245,265)(246,268)(247,267)(248,266)(249,261)
(250,264)(251,263)(252,262)(253,269)(254,272)(255,271)(256,270)(274,276)
(277,281)(278,284)(279,283)(280,282)(286,288);
s2 := Sym(290)!( 1,145)( 2,146)( 3,148)( 4,147)( 5,157)( 6,158)( 7,160)
( 8,159)( 9,153)( 10,154)( 11,156)( 12,155)( 13,149)( 14,150)( 15,152)
( 16,151)( 17,177)( 18,178)( 19,180)( 20,179)( 21,189)( 22,190)( 23,192)
( 24,191)( 25,185)( 26,186)( 27,188)( 28,187)( 29,181)( 30,182)( 31,184)
( 32,183)( 33,161)( 34,162)( 35,164)( 36,163)( 37,173)( 38,174)( 39,176)
( 40,175)( 41,169)( 42,170)( 43,172)( 44,171)( 45,165)( 46,166)( 47,168)
( 48,167)( 49,257)( 50,258)( 51,260)( 52,259)( 53,269)( 54,270)( 55,272)
( 56,271)( 57,265)( 58,266)( 59,268)( 60,267)( 61,261)( 62,262)( 63,264)
( 64,263)( 65,241)( 66,242)( 67,244)( 68,243)( 69,253)( 70,254)( 71,256)
( 72,255)( 73,249)( 74,250)( 75,252)( 76,251)( 77,245)( 78,246)( 79,248)
( 80,247)( 81,273)( 82,274)( 83,276)( 84,275)( 85,285)( 86,286)( 87,288)
( 88,287)( 89,281)( 90,282)( 91,284)( 92,283)( 93,277)( 94,278)( 95,280)
( 96,279)( 97,209)( 98,210)( 99,212)(100,211)(101,221)(102,222)(103,224)
(104,223)(105,217)(106,218)(107,220)(108,219)(109,213)(110,214)(111,216)
(112,215)(113,193)(114,194)(115,196)(116,195)(117,205)(118,206)(119,208)
(120,207)(121,201)(122,202)(123,204)(124,203)(125,197)(126,198)(127,200)
(128,199)(129,225)(130,226)(131,228)(132,227)(133,237)(134,238)(135,240)
(136,239)(137,233)(138,234)(139,236)(140,235)(141,229)(142,230)(143,232)
(144,231);
s3 := Sym(290)!( 1, 3)( 2, 4)( 5, 7)( 6, 8)( 9, 11)( 10, 12)( 13, 15)
( 14, 16)( 17, 19)( 18, 20)( 21, 23)( 22, 24)( 25, 27)( 26, 28)( 29, 31)
( 30, 32)( 33, 35)( 34, 36)( 37, 39)( 38, 40)( 41, 43)( 42, 44)( 45, 47)
( 46, 48)( 49, 51)( 50, 52)( 53, 55)( 54, 56)( 57, 59)( 58, 60)( 61, 63)
( 62, 64)( 65, 67)( 66, 68)( 69, 71)( 70, 72)( 73, 75)( 74, 76)( 77, 79)
( 78, 80)( 81, 83)( 82, 84)( 85, 87)( 86, 88)( 89, 91)( 90, 92)( 93, 95)
( 94, 96)( 97, 99)( 98,100)(101,103)(102,104)(105,107)(106,108)(109,111)
(110,112)(113,115)(114,116)(117,119)(118,120)(121,123)(122,124)(125,127)
(126,128)(129,131)(130,132)(133,135)(134,136)(137,139)(138,140)(141,143)
(142,144)(145,147)(146,148)(149,151)(150,152)(153,155)(154,156)(157,159)
(158,160)(161,163)(162,164)(165,167)(166,168)(169,171)(170,172)(173,175)
(174,176)(177,179)(178,180)(181,183)(182,184)(185,187)(186,188)(189,191)
(190,192)(193,195)(194,196)(197,199)(198,200)(201,203)(202,204)(205,207)
(206,208)(209,211)(210,212)(213,215)(214,216)(217,219)(218,220)(221,223)
(222,224)(225,227)(226,228)(229,231)(230,232)(233,235)(234,236)(237,239)
(238,240)(241,243)(242,244)(245,247)(246,248)(249,251)(250,252)(253,255)
(254,256)(257,259)(258,260)(261,263)(262,264)(265,267)(266,268)(269,271)
(270,272)(273,275)(274,276)(277,279)(278,280)(281,283)(282,284)(285,287)
(286,288);
s4 := Sym(290)!(289,290);
poly := sub<Sym(290)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s0*s2*s0*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4,
s2*s4*s2*s4, s3*s4*s3*s4, s0*s1*s0*s1*s0*s1*s0*s1,
s2*s3*s2*s3*s2*s3*s2*s3, s0*s1*s2*s1*s0*s1*s2*s0*s1,
s3*s2*s1*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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
to this polytope