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