Polytope of Type {46,18}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {46,18}*1656
Also Known As : {46,18|2}. if this polytope has another name.
Group : SmallGroup(1656,40)
Rank : 3
Schlafli Type : {46,18}
Number of vertices, edges, etc : 46, 414, 18
Order of s0s1s2 : 414
Order of s0s1s2s1 : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   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) :
   3-fold quotients : {46,6}*552
   9-fold quotients : {46,2}*184
   18-fold quotients : {23,2}*92
   23-fold quotients : {2,18}*72
   46-fold quotients : {2,9}*36
   69-fold quotients : {2,6}*24
   138-fold quotients : {2,3}*12
   207-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Irregular Quotients (of which this is a minimal cover):
   None.

Permutation Representation (GAP) : 
s0 := (  4, 67)(  5, 68)(  6, 69)(  7, 64)(  8, 65)(  9, 66)( 10, 61)( 11, 62)( 12, 63)( 13, 58)( 14, 59)( 15, 60)( 16, 55)( 17, 56)( 18, 57)( 19, 52)( 20, 53)( 21, 54)( 22, 49)( 23, 50)( 24, 51)( 25, 46)( 26, 47)( 27, 48)( 28, 43)( 29, 44)( 30, 45)( 31, 40)( 32, 41)( 33, 42)( 34, 37)( 35, 38)( 36, 39)( 73,136)( 74,137)( 75,138)( 76,133)( 77,134)( 78,135)( 79,130)( 80,131)( 81,132)( 82,127)( 83,128)( 84,129)( 85,124)( 86,125)( 87,126)( 88,121)( 89,122)( 90,123)( 91,118)( 92,119)( 93,120)( 94,115)( 95,116)( 96,117)( 97,112)( 98,113)( 99,114)(100,109)(101,110)(102,111)(103,106)(104,107)(105,108)(142,205)(143,206)(144,207)(145,202)(146,203)(147,204)(148,199)(149,200)(150,201)(151,196)(152,197)(153,198)(154,193)(155,194)(156,195)(157,190)(158,191)(159,192)(160,187)(161,188)(162,189)(163,184)(164,185)(165,186)(166,181)(167,182)(168,183)(169,178)(170,179)(171,180)(172,175)(173,176)(174,177)(211,274)(212,275)(213,276)(214,271)(215,272)(216,273)(217,268)(218,269)(219,270)(220,265)(221,266)(222,267)(223,262)(224,263)(225,264)(226,259)(227,260)(228,261)(229,256)(230,257)(231,258)(232,253)(233,254)(234,255)(235,250)(236,251)(237,252)(238,247)(239,248)(240,249)(241,244)(242,245)(243,246)(280,343)(281,344)(282,345)(283,340)(284,341)(285,342)(286,337)(287,338)(288,339)(289,334)(290,335)(291,336)(292,331)(293,332)(294,333)(295,328)(296,329)(297,330)(298,325)(299,326)(300,327)(301,322)(302,323)(303,324)(304,319)(305,320)(306,321)(307,316)(308,317)(309,318)(310,313)(311,314)(312,315)(349,412)(350,413)(351,414)(352,409)(353,410)(354,411)(355,406)(356,407)(357,408)(358,403)(359,404)(360,405)(361,400)(362,401)(363,402)(364,397)(365,398)(366,399)(367,394)(368,395)(369,396)(370,391)(371,392)(372,393)(373,388)(374,389)(375,390)(376,385)(377,386)(378,387)(379,382)(380,383)(381,384);;
s1 := (  1,  4)(  2,  6)(  3,  5)(  7, 67)(  8, 69)(  9, 68)( 10, 64)( 11, 66)( 12, 65)( 13, 61)( 14, 63)( 15, 62)( 16, 58)( 17, 60)( 18, 59)( 19, 55)( 20, 57)( 21, 56)( 22, 52)( 23, 54)( 24, 53)( 25, 49)( 26, 51)( 27, 50)( 28, 46)( 29, 48)( 30, 47)( 31, 43)( 32, 45)( 33, 44)( 34, 40)( 35, 42)( 36, 41)( 38, 39)( 70,143)( 71,142)( 72,144)( 73,140)( 74,139)( 75,141)( 76,206)( 77,205)( 78,207)( 79,203)( 80,202)( 81,204)( 82,200)( 83,199)( 84,201)( 85,197)( 86,196)( 87,198)( 88,194)( 89,193)( 90,195)( 91,191)( 92,190)( 93,192)( 94,188)( 95,187)( 96,189)( 97,185)( 98,184)( 99,186)(100,182)(101,181)(102,183)(103,179)(104,178)(105,180)(106,176)(107,175)(108,177)(109,173)(110,172)(111,174)(112,170)(113,169)(114,171)(115,167)(116,166)(117,168)(118,164)(119,163)(120,165)(121,161)(122,160)(123,162)(124,158)(125,157)(126,159)(127,155)(128,154)(129,156)(130,152)(131,151)(132,153)(133,149)(134,148)(135,150)(136,146)(137,145)(138,147)(208,211)(209,213)(210,212)(214,274)(215,276)(216,275)(217,271)(218,273)(219,272)(220,268)(221,270)(222,269)(223,265)(224,267)(225,266)(226,262)(227,264)(228,263)(229,259)(230,261)(231,260)(232,256)(233,258)(234,257)(235,253)(236,255)(237,254)(238,250)(239,252)(240,251)(241,247)(242,249)(243,248)(245,246)(277,350)(278,349)(279,351)(280,347)(281,346)(282,348)(283,413)(284,412)(285,414)(286,410)(287,409)(288,411)(289,407)(290,406)(291,408)(292,404)(293,403)(294,405)(295,401)(296,400)(297,402)(298,398)(299,397)(300,399)(301,395)(302,394)(303,396)(304,392)(305,391)(306,393)(307,389)(308,388)(309,390)(310,386)(311,385)(312,387)(313,383)(314,382)(315,384)(316,380)(317,379)(318,381)(319,377)(320,376)(321,378)(322,374)(323,373)(324,375)(325,371)(326,370)(327,372)(328,368)(329,367)(330,369)(331,365)(332,364)(333,366)(334,362)(335,361)(336,363)(337,359)(338,358)(339,360)(340,356)(341,355)(342,357)(343,353)(344,352)(345,354);;
s2 := (  1,277)(  2,279)(  3,278)(  4,280)(  5,282)(  6,281)(  7,283)(  8,285)(  9,284)( 10,286)( 11,288)( 12,287)( 13,289)( 14,291)( 15,290)( 16,292)( 17,294)( 18,293)( 19,295)( 20,297)( 21,296)( 22,298)( 23,300)( 24,299)( 25,301)( 26,303)( 27,302)( 28,304)( 29,306)( 30,305)( 31,307)( 32,309)( 33,308)( 34,310)( 35,312)( 36,311)( 37,313)( 38,315)( 39,314)( 40,316)( 41,318)( 42,317)( 43,319)( 44,321)( 45,320)( 46,322)( 47,324)( 48,323)( 49,325)( 50,327)( 51,326)( 52,328)( 53,330)( 54,329)( 55,331)( 56,333)( 57,332)( 58,334)( 59,336)( 60,335)( 61,337)( 62,339)( 63,338)( 64,340)( 65,342)( 66,341)( 67,343)( 68,345)( 69,344)( 70,208)( 71,210)( 72,209)( 73,211)( 74,213)( 75,212)( 76,214)( 77,216)( 78,215)( 79,217)( 80,219)( 81,218)( 82,220)( 83,222)( 84,221)( 85,223)( 86,225)( 87,224)( 88,226)( 89,228)( 90,227)( 91,229)( 92,231)( 93,230)( 94,232)( 95,234)( 96,233)( 97,235)( 98,237)( 99,236)(100,238)(101,240)(102,239)(103,241)(104,243)(105,242)(106,244)(107,246)(108,245)(109,247)(110,249)(111,248)(112,250)(113,252)(114,251)(115,253)(116,255)(117,254)(118,256)(119,258)(120,257)(121,259)(122,261)(123,260)(124,262)(125,264)(126,263)(127,265)(128,267)(129,266)(130,268)(131,270)(132,269)(133,271)(134,273)(135,272)(136,274)(137,276)(138,275)(139,347)(140,346)(141,348)(142,350)(143,349)(144,351)(145,353)(146,352)(147,354)(148,356)(149,355)(150,357)(151,359)(152,358)(153,360)(154,362)(155,361)(156,363)(157,365)(158,364)(159,366)(160,368)(161,367)(162,369)(163,371)(164,370)(165,372)(166,374)(167,373)(168,375)(169,377)(170,376)(171,378)(172,380)(173,379)(174,381)(175,383)(176,382)(177,384)(178,386)(179,385)(180,387)(181,389)(182,388)(183,390)(184,392)(185,391)(186,393)(187,395)(188,394)(189,396)(190,398)(191,397)(192,399)(193,401)(194,400)(195,402)(196,404)(197,403)(198,405)(199,407)(200,406)(201,408)(202,410)(203,409)(204,411)(205,413)(206,412)(207,414);;
poly := Group([s0,s1,s2]);;
Finitely Presented Group Representation (GAP) : 
F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s2*s1*s0*s1*s2*s1, 
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, 
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*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) : 
s0 := Sym(414)!(  4, 67)(  5, 68)(  6, 69)(  7, 64)(  8, 65)(  9, 66)( 10, 61)( 11, 62)( 12, 63)( 13, 58)( 14, 59)( 15, 60)( 16, 55)( 17, 56)( 18, 57)( 19, 52)( 20, 53)( 21, 54)( 22, 49)( 23, 50)( 24, 51)( 25, 46)( 26, 47)( 27, 48)( 28, 43)( 29, 44)( 30, 45)( 31, 40)( 32, 41)( 33, 42)( 34, 37)( 35, 38)( 36, 39)( 73,136)( 74,137)( 75,138)( 76,133)( 77,134)( 78,135)( 79,130)( 80,131)( 81,132)( 82,127)( 83,128)( 84,129)( 85,124)( 86,125)( 87,126)( 88,121)( 89,122)( 90,123)( 91,118)( 92,119)( 93,120)( 94,115)( 95,116)( 96,117)( 97,112)( 98,113)( 99,114)(100,109)(101,110)(102,111)(103,106)(104,107)(105,108)(142,205)(143,206)(144,207)(145,202)(146,203)(147,204)(148,199)(149,200)(150,201)(151,196)(152,197)(153,198)(154,193)(155,194)(156,195)(157,190)(158,191)(159,192)(160,187)(161,188)(162,189)(163,184)(164,185)(165,186)(166,181)(167,182)(168,183)(169,178)(170,179)(171,180)(172,175)(173,176)(174,177)(211,274)(212,275)(213,276)(214,271)(215,272)(216,273)(217,268)(218,269)(219,270)(220,265)(221,266)(222,267)(223,262)(224,263)(225,264)(226,259)(227,260)(228,261)(229,256)(230,257)(231,258)(232,253)(233,254)(234,255)(235,250)(236,251)(237,252)(238,247)(239,248)(240,249)(241,244)(242,245)(243,246)(280,343)(281,344)(282,345)(283,340)(284,341)(285,342)(286,337)(287,338)(288,339)(289,334)(290,335)(291,336)(292,331)(293,332)(294,333)(295,328)(296,329)(297,330)(298,325)(299,326)(300,327)(301,322)(302,323)(303,324)(304,319)(305,320)(306,321)(307,316)(308,317)(309,318)(310,313)(311,314)(312,315)(349,412)(350,413)(351,414)(352,409)(353,410)(354,411)(355,406)(356,407)(357,408)(358,403)(359,404)(360,405)(361,400)(362,401)(363,402)(364,397)(365,398)(366,399)(367,394)(368,395)(369,396)(370,391)(371,392)(372,393)(373,388)(374,389)(375,390)(376,385)(377,386)(378,387)(379,382)(380,383)(381,384);
s1 := Sym(414)!(  1,  4)(  2,  6)(  3,  5)(  7, 67)(  8, 69)(  9, 68)( 10, 64)( 11, 66)( 12, 65)( 13, 61)( 14, 63)( 15, 62)( 16, 58)( 17, 60)( 18, 59)( 19, 55)( 20, 57)( 21, 56)( 22, 52)( 23, 54)( 24, 53)( 25, 49)( 26, 51)( 27, 50)( 28, 46)( 29, 48)( 30, 47)( 31, 43)( 32, 45)( 33, 44)( 34, 40)( 35, 42)( 36, 41)( 38, 39)( 70,143)( 71,142)( 72,144)( 73,140)( 74,139)( 75,141)( 76,206)( 77,205)( 78,207)( 79,203)( 80,202)( 81,204)( 82,200)( 83,199)( 84,201)( 85,197)( 86,196)( 87,198)( 88,194)( 89,193)( 90,195)( 91,191)( 92,190)( 93,192)( 94,188)( 95,187)( 96,189)( 97,185)( 98,184)( 99,186)(100,182)(101,181)(102,183)(103,179)(104,178)(105,180)(106,176)(107,175)(108,177)(109,173)(110,172)(111,174)(112,170)(113,169)(114,171)(115,167)(116,166)(117,168)(118,164)(119,163)(120,165)(121,161)(122,160)(123,162)(124,158)(125,157)(126,159)(127,155)(128,154)(129,156)(130,152)(131,151)(132,153)(133,149)(134,148)(135,150)(136,146)(137,145)(138,147)(208,211)(209,213)(210,212)(214,274)(215,276)(216,275)(217,271)(218,273)(219,272)(220,268)(221,270)(222,269)(223,265)(224,267)(225,266)(226,262)(227,264)(228,263)(229,259)(230,261)(231,260)(232,256)(233,258)(234,257)(235,253)(236,255)(237,254)(238,250)(239,252)(240,251)(241,247)(242,249)(243,248)(245,246)(277,350)(278,349)(279,351)(280,347)(281,346)(282,348)(283,413)(284,412)(285,414)(286,410)(287,409)(288,411)(289,407)(290,406)(291,408)(292,404)(293,403)(294,405)(295,401)(296,400)(297,402)(298,398)(299,397)(300,399)(301,395)(302,394)(303,396)(304,392)(305,391)(306,393)(307,389)(308,388)(309,390)(310,386)(311,385)(312,387)(313,383)(314,382)(315,384)(316,380)(317,379)(318,381)(319,377)(320,376)(321,378)(322,374)(323,373)(324,375)(325,371)(326,370)(327,372)(328,368)(329,367)(330,369)(331,365)(332,364)(333,366)(334,362)(335,361)(336,363)(337,359)(338,358)(339,360)(340,356)(341,355)(342,357)(343,353)(344,352)(345,354);
s2 := Sym(414)!(  1,277)(  2,279)(  3,278)(  4,280)(  5,282)(  6,281)(  7,283)(  8,285)(  9,284)( 10,286)( 11,288)( 12,287)( 13,289)( 14,291)( 15,290)( 16,292)( 17,294)( 18,293)( 19,295)( 20,297)( 21,296)( 22,298)( 23,300)( 24,299)( 25,301)( 26,303)( 27,302)( 28,304)( 29,306)( 30,305)( 31,307)( 32,309)( 33,308)( 34,310)( 35,312)( 36,311)( 37,313)( 38,315)( 39,314)( 40,316)( 41,318)( 42,317)( 43,319)( 44,321)( 45,320)( 46,322)( 47,324)( 48,323)( 49,325)( 50,327)( 51,326)( 52,328)( 53,330)( 54,329)( 55,331)( 56,333)( 57,332)( 58,334)( 59,336)( 60,335)( 61,337)( 62,339)( 63,338)( 64,340)( 65,342)( 66,341)( 67,343)( 68,345)( 69,344)( 70,208)( 71,210)( 72,209)( 73,211)( 74,213)( 75,212)( 76,214)( 77,216)( 78,215)( 79,217)( 80,219)( 81,218)( 82,220)( 83,222)( 84,221)( 85,223)( 86,225)( 87,224)( 88,226)( 89,228)( 90,227)( 91,229)( 92,231)( 93,230)( 94,232)( 95,234)( 96,233)( 97,235)( 98,237)( 99,236)(100,238)(101,240)(102,239)(103,241)(104,243)(105,242)(106,244)(107,246)(108,245)(109,247)(110,249)(111,248)(112,250)(113,252)(114,251)(115,253)(116,255)(117,254)(118,256)(119,258)(120,257)(121,259)(122,261)(123,260)(124,262)(125,264)(126,263)(127,265)(128,267)(129,266)(130,268)(131,270)(132,269)(133,271)(134,273)(135,272)(136,274)(137,276)(138,275)(139,347)(140,346)(141,348)(142,350)(143,349)(144,351)(145,353)(146,352)(147,354)(148,356)(149,355)(150,357)(151,359)(152,358)(153,360)(154,362)(155,361)(156,363)(157,365)(158,364)(159,366)(160,368)(161,367)(162,369)(163,371)(164,370)(165,372)(166,374)(167,373)(168,375)(169,377)(170,376)(171,378)(172,380)(173,379)(174,381)(175,383)(176,382)(177,384)(178,386)(179,385)(180,387)(181,389)(182,388)(183,390)(184,392)(185,391)(186,393)(187,395)(188,394)(189,396)(190,398)(191,397)(192,399)(193,401)(194,400)(195,402)(196,404)(197,403)(198,405)(199,407)(200,406)(201,408)(202,410)(203,409)(204,411)(205,413)(206,412)(207,414);
poly := sub<Sym(414)|s0,s1,s2>;
Finitely Presented Group Representation (Magma) : 
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s0*s1*s2*s1*s0*s1*s2*s1, 
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, 
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*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope

Twisty Puzzle