Polytope of Type {24,18}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24,18}*1728a
if this polytope has a name.
Group : SmallGroup(1728,12315)
Rank : 3
Schlafli Type : {24,18}
Number of vertices, edges, etc : 48, 432, 36
Order of s0s1s2 : 9
Order of s0s1s2s1 : 8
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
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 : {8,18}*576a, {24,6}*576a
   4-fold quotients : {12,18}*432c
   9-fold quotients : {8,6}*192a
   12-fold quotients : {4,18}*144c, {12,6}*144d
   24-fold quotients : {4,9}*72
   36-fold quotients : {4,6}*48b
   72-fold quotients : {4,3}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s0*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s2> of order 2.
      24 facets:
         12 of {12}*24
         12 of {24}*48
      24 vertex figures:
         24 of {18}*36

Permutation Representation (GAP) : 
s0 := (  1,  9)(  2, 10)(  3, 11)(  4, 12)(  5, 14)(  6, 13)(  7, 16)(  8, 15)( 17, 25)( 18, 26)( 19, 27)( 20, 28)( 21, 30)( 22, 29)( 23, 32)( 24, 31)( 33, 41)( 34, 42)( 35, 43)( 36, 44)( 37, 46)( 38, 45)( 39, 48)( 40, 47)( 49,105)( 50,106)( 51,107)( 52,108)( 53,110)( 54,109)( 55,112)( 56,111)( 57, 97)( 58, 98)( 59, 99)( 60,100)( 61,102)( 62,101)( 63,104)( 64,103)( 65,121)( 66,122)( 67,123)( 68,124)( 69,126)( 70,125)( 71,128)( 72,127)( 73,113)( 74,114)( 75,115)( 76,116)( 77,118)( 78,117)( 79,120)( 80,119)( 81,137)( 82,138)( 83,139)( 84,140)( 85,142)( 86,141)( 87,144)( 88,143)( 89,129)( 90,130)( 91,131)( 92,132)( 93,134)( 94,133)( 95,136)( 96,135)(145,153)(146,154)(147,155)(148,156)(149,158)(150,157)(151,160)(152,159)(161,169)(162,170)(163,171)(164,172)(165,174)(166,173)(167,176)(168,175)(177,185)(178,186)(179,187)(180,188)(181,190)(182,189)(183,192)(184,191)(193,249)(194,250)(195,251)(196,252)(197,254)(198,253)(199,256)(200,255)(201,241)(202,242)(203,243)(204,244)(205,246)(206,245)(207,248)(208,247)(209,265)(210,266)(211,267)(212,268)(213,270)(214,269)(215,272)(216,271)(217,257)(218,258)(219,259)(220,260)(221,262)(222,261)(223,264)(224,263)(225,281)(226,282)(227,283)(228,284)(229,286)(230,285)(231,288)(232,287)(233,273)(234,274)(235,275)(236,276)(237,278)(238,277)(239,280)(240,279)(289,297)(290,298)(291,299)(292,300)(293,302)(294,301)(295,304)(296,303)(305,313)(306,314)(307,315)(308,316)(309,318)(310,317)(311,320)(312,319)(321,329)(322,330)(323,331)(324,332)(325,334)(326,333)(327,336)(328,335)(337,393)(338,394)(339,395)(340,396)(341,398)(342,397)(343,400)(344,399)(345,385)(346,386)(347,387)(348,388)(349,390)(350,389)(351,392)(352,391)(353,409)(354,410)(355,411)(356,412)(357,414)(358,413)(359,416)(360,415)(361,401)(362,402)(363,403)(364,404)(365,406)(366,405)(367,408)(368,407)(369,425)(370,426)(371,427)(372,428)(373,430)(374,429)(375,432)(376,431)(377,417)(378,418)(379,419)(380,420)(381,422)(382,421)(383,424)(384,423);;
s1 := (  1, 49)(  2, 50)(  3, 52)(  4, 51)(  5, 53)(  6, 54)(  7, 56)(  8, 55)(  9, 63)( 10, 64)( 11, 62)( 12, 61)( 13, 60)( 14, 59)( 15, 57)( 16, 58)( 17, 81)( 18, 82)( 19, 84)( 20, 83)( 21, 85)( 22, 86)( 23, 88)( 24, 87)( 25, 95)( 26, 96)( 27, 94)( 28, 93)( 29, 92)( 30, 91)( 31, 89)( 32, 90)( 33, 65)( 34, 66)( 35, 68)( 36, 67)( 37, 69)( 38, 70)( 39, 72)( 40, 71)( 41, 79)( 42, 80)( 43, 78)( 44, 77)( 45, 76)( 46, 75)( 47, 73)( 48, 74)( 99,100)(103,104)(105,111)(106,112)(107,110)(108,109)(113,129)(114,130)(115,132)(116,131)(117,133)(118,134)(119,136)(120,135)(121,143)(122,144)(123,142)(124,141)(125,140)(126,139)(127,137)(128,138)(145,369)(146,370)(147,372)(148,371)(149,373)(150,374)(151,376)(152,375)(153,383)(154,384)(155,382)(156,381)(157,380)(158,379)(159,377)(160,378)(161,353)(162,354)(163,356)(164,355)(165,357)(166,358)(167,360)(168,359)(169,367)(170,368)(171,366)(172,365)(173,364)(174,363)(175,361)(176,362)(177,337)(178,338)(179,340)(180,339)(181,341)(182,342)(183,344)(184,343)(185,351)(186,352)(187,350)(188,349)(189,348)(190,347)(191,345)(192,346)(193,321)(194,322)(195,324)(196,323)(197,325)(198,326)(199,328)(200,327)(201,335)(202,336)(203,334)(204,333)(205,332)(206,331)(207,329)(208,330)(209,305)(210,306)(211,308)(212,307)(213,309)(214,310)(215,312)(216,311)(217,319)(218,320)(219,318)(220,317)(221,316)(222,315)(223,313)(224,314)(225,289)(226,290)(227,292)(228,291)(229,293)(230,294)(231,296)(232,295)(233,303)(234,304)(235,302)(236,301)(237,300)(238,299)(239,297)(240,298)(241,417)(242,418)(243,420)(244,419)(245,421)(246,422)(247,424)(248,423)(249,431)(250,432)(251,430)(252,429)(253,428)(254,427)(255,425)(256,426)(257,401)(258,402)(259,404)(260,403)(261,405)(262,406)(263,408)(264,407)(265,415)(266,416)(267,414)(268,413)(269,412)(270,411)(271,409)(272,410)(273,385)(274,386)(275,388)(276,387)(277,389)(278,390)(279,392)(280,391)(281,399)(282,400)(283,398)(284,397)(285,396)(286,395)(287,393)(288,394);;
s2 := (  1,145)(  2,148)(  3,147)(  4,146)(  5,160)(  6,157)(  7,158)(  8,159)(  9,153)( 10,156)( 11,155)( 12,154)( 13,150)( 14,151)( 15,152)( 16,149)( 17,177)( 18,180)( 19,179)( 20,178)( 21,192)( 22,189)( 23,190)( 24,191)( 25,185)( 26,188)( 27,187)( 28,186)( 29,182)( 30,183)( 31,184)( 32,181)( 33,161)( 34,164)( 35,163)( 36,162)( 37,176)( 38,173)( 39,174)( 40,175)( 41,169)( 42,172)( 43,171)( 44,170)( 45,166)( 46,167)( 47,168)( 48,165)( 49,193)( 50,196)( 51,195)( 52,194)( 53,208)( 54,205)( 55,206)( 56,207)( 57,201)( 58,204)( 59,203)( 60,202)( 61,198)( 62,199)( 63,200)( 64,197)( 65,225)( 66,228)( 67,227)( 68,226)( 69,240)( 70,237)( 71,238)( 72,239)( 73,233)( 74,236)( 75,235)( 76,234)( 77,230)( 78,231)( 79,232)( 80,229)( 81,209)( 82,212)( 83,211)( 84,210)( 85,224)( 86,221)( 87,222)( 88,223)( 89,217)( 90,220)( 91,219)( 92,218)( 93,214)( 94,215)( 95,216)( 96,213)( 97,241)( 98,244)( 99,243)(100,242)(101,256)(102,253)(103,254)(104,255)(105,249)(106,252)(107,251)(108,250)(109,246)(110,247)(111,248)(112,245)(113,273)(114,276)(115,275)(116,274)(117,288)(118,285)(119,286)(120,287)(121,281)(122,284)(123,283)(124,282)(125,278)(126,279)(127,280)(128,277)(129,257)(130,260)(131,259)(132,258)(133,272)(134,269)(135,270)(136,271)(137,265)(138,268)(139,267)(140,266)(141,262)(142,263)(143,264)(144,261)(289,321)(290,324)(291,323)(292,322)(293,336)(294,333)(295,334)(296,335)(297,329)(298,332)(299,331)(300,330)(301,326)(302,327)(303,328)(304,325)(306,308)(309,320)(310,317)(311,318)(312,319)(314,316)(337,369)(338,372)(339,371)(340,370)(341,384)(342,381)(343,382)(344,383)(345,377)(346,380)(347,379)(348,378)(349,374)(350,375)(351,376)(352,373)(354,356)(357,368)(358,365)(359,366)(360,367)(362,364)(385,417)(386,420)(387,419)(388,418)(389,432)(390,429)(391,430)(392,431)(393,425)(394,428)(395,427)(396,426)(397,422)(398,423)(399,424)(400,421)(402,404)(405,416)(406,413)(407,414)(408,415)(410,412);;
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*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1, 
s2*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1*s0, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) : 
s0 := Sym(432)!(  1,  9)(  2, 10)(  3, 11)(  4, 12)(  5, 14)(  6, 13)(  7, 16)(  8, 15)( 17, 25)( 18, 26)( 19, 27)( 20, 28)( 21, 30)( 22, 29)( 23, 32)( 24, 31)( 33, 41)( 34, 42)( 35, 43)( 36, 44)( 37, 46)( 38, 45)( 39, 48)( 40, 47)( 49,105)( 50,106)( 51,107)( 52,108)( 53,110)( 54,109)( 55,112)( 56,111)( 57, 97)( 58, 98)( 59, 99)( 60,100)( 61,102)( 62,101)( 63,104)( 64,103)( 65,121)( 66,122)( 67,123)( 68,124)( 69,126)( 70,125)( 71,128)( 72,127)( 73,113)( 74,114)( 75,115)( 76,116)( 77,118)( 78,117)( 79,120)( 80,119)( 81,137)( 82,138)( 83,139)( 84,140)( 85,142)( 86,141)( 87,144)( 88,143)( 89,129)( 90,130)( 91,131)( 92,132)( 93,134)( 94,133)( 95,136)( 96,135)(145,153)(146,154)(147,155)(148,156)(149,158)(150,157)(151,160)(152,159)(161,169)(162,170)(163,171)(164,172)(165,174)(166,173)(167,176)(168,175)(177,185)(178,186)(179,187)(180,188)(181,190)(182,189)(183,192)(184,191)(193,249)(194,250)(195,251)(196,252)(197,254)(198,253)(199,256)(200,255)(201,241)(202,242)(203,243)(204,244)(205,246)(206,245)(207,248)(208,247)(209,265)(210,266)(211,267)(212,268)(213,270)(214,269)(215,272)(216,271)(217,257)(218,258)(219,259)(220,260)(221,262)(222,261)(223,264)(224,263)(225,281)(226,282)(227,283)(228,284)(229,286)(230,285)(231,288)(232,287)(233,273)(234,274)(235,275)(236,276)(237,278)(238,277)(239,280)(240,279)(289,297)(290,298)(291,299)(292,300)(293,302)(294,301)(295,304)(296,303)(305,313)(306,314)(307,315)(308,316)(309,318)(310,317)(311,320)(312,319)(321,329)(322,330)(323,331)(324,332)(325,334)(326,333)(327,336)(328,335)(337,393)(338,394)(339,395)(340,396)(341,398)(342,397)(343,400)(344,399)(345,385)(346,386)(347,387)(348,388)(349,390)(350,389)(351,392)(352,391)(353,409)(354,410)(355,411)(356,412)(357,414)(358,413)(359,416)(360,415)(361,401)(362,402)(363,403)(364,404)(365,406)(366,405)(367,408)(368,407)(369,425)(370,426)(371,427)(372,428)(373,430)(374,429)(375,432)(376,431)(377,417)(378,418)(379,419)(380,420)(381,422)(382,421)(383,424)(384,423);
s1 := Sym(432)!(  1, 49)(  2, 50)(  3, 52)(  4, 51)(  5, 53)(  6, 54)(  7, 56)(  8, 55)(  9, 63)( 10, 64)( 11, 62)( 12, 61)( 13, 60)( 14, 59)( 15, 57)( 16, 58)( 17, 81)( 18, 82)( 19, 84)( 20, 83)( 21, 85)( 22, 86)( 23, 88)( 24, 87)( 25, 95)( 26, 96)( 27, 94)( 28, 93)( 29, 92)( 30, 91)( 31, 89)( 32, 90)( 33, 65)( 34, 66)( 35, 68)( 36, 67)( 37, 69)( 38, 70)( 39, 72)( 40, 71)( 41, 79)( 42, 80)( 43, 78)( 44, 77)( 45, 76)( 46, 75)( 47, 73)( 48, 74)( 99,100)(103,104)(105,111)(106,112)(107,110)(108,109)(113,129)(114,130)(115,132)(116,131)(117,133)(118,134)(119,136)(120,135)(121,143)(122,144)(123,142)(124,141)(125,140)(126,139)(127,137)(128,138)(145,369)(146,370)(147,372)(148,371)(149,373)(150,374)(151,376)(152,375)(153,383)(154,384)(155,382)(156,381)(157,380)(158,379)(159,377)(160,378)(161,353)(162,354)(163,356)(164,355)(165,357)(166,358)(167,360)(168,359)(169,367)(170,368)(171,366)(172,365)(173,364)(174,363)(175,361)(176,362)(177,337)(178,338)(179,340)(180,339)(181,341)(182,342)(183,344)(184,343)(185,351)(186,352)(187,350)(188,349)(189,348)(190,347)(191,345)(192,346)(193,321)(194,322)(195,324)(196,323)(197,325)(198,326)(199,328)(200,327)(201,335)(202,336)(203,334)(204,333)(205,332)(206,331)(207,329)(208,330)(209,305)(210,306)(211,308)(212,307)(213,309)(214,310)(215,312)(216,311)(217,319)(218,320)(219,318)(220,317)(221,316)(222,315)(223,313)(224,314)(225,289)(226,290)(227,292)(228,291)(229,293)(230,294)(231,296)(232,295)(233,303)(234,304)(235,302)(236,301)(237,300)(238,299)(239,297)(240,298)(241,417)(242,418)(243,420)(244,419)(245,421)(246,422)(247,424)(248,423)(249,431)(250,432)(251,430)(252,429)(253,428)(254,427)(255,425)(256,426)(257,401)(258,402)(259,404)(260,403)(261,405)(262,406)(263,408)(264,407)(265,415)(266,416)(267,414)(268,413)(269,412)(270,411)(271,409)(272,410)(273,385)(274,386)(275,388)(276,387)(277,389)(278,390)(279,392)(280,391)(281,399)(282,400)(283,398)(284,397)(285,396)(286,395)(287,393)(288,394);
s2 := Sym(432)!(  1,145)(  2,148)(  3,147)(  4,146)(  5,160)(  6,157)(  7,158)(  8,159)(  9,153)( 10,156)( 11,155)( 12,154)( 13,150)( 14,151)( 15,152)( 16,149)( 17,177)( 18,180)( 19,179)( 20,178)( 21,192)( 22,189)( 23,190)( 24,191)( 25,185)( 26,188)( 27,187)( 28,186)( 29,182)( 30,183)( 31,184)( 32,181)( 33,161)( 34,164)( 35,163)( 36,162)( 37,176)( 38,173)( 39,174)( 40,175)( 41,169)( 42,172)( 43,171)( 44,170)( 45,166)( 46,167)( 47,168)( 48,165)( 49,193)( 50,196)( 51,195)( 52,194)( 53,208)( 54,205)( 55,206)( 56,207)( 57,201)( 58,204)( 59,203)( 60,202)( 61,198)( 62,199)( 63,200)( 64,197)( 65,225)( 66,228)( 67,227)( 68,226)( 69,240)( 70,237)( 71,238)( 72,239)( 73,233)( 74,236)( 75,235)( 76,234)( 77,230)( 78,231)( 79,232)( 80,229)( 81,209)( 82,212)( 83,211)( 84,210)( 85,224)( 86,221)( 87,222)( 88,223)( 89,217)( 90,220)( 91,219)( 92,218)( 93,214)( 94,215)( 95,216)( 96,213)( 97,241)( 98,244)( 99,243)(100,242)(101,256)(102,253)(103,254)(104,255)(105,249)(106,252)(107,251)(108,250)(109,246)(110,247)(111,248)(112,245)(113,273)(114,276)(115,275)(116,274)(117,288)(118,285)(119,286)(120,287)(121,281)(122,284)(123,283)(124,282)(125,278)(126,279)(127,280)(128,277)(129,257)(130,260)(131,259)(132,258)(133,272)(134,269)(135,270)(136,271)(137,265)(138,268)(139,267)(140,266)(141,262)(142,263)(143,264)(144,261)(289,321)(290,324)(291,323)(292,322)(293,336)(294,333)(295,334)(296,335)(297,329)(298,332)(299,331)(300,330)(301,326)(302,327)(303,328)(304,325)(306,308)(309,320)(310,317)(311,318)(312,319)(314,316)(337,369)(338,372)(339,371)(340,370)(341,384)(342,381)(343,382)(344,383)(345,377)(346,380)(347,379)(348,378)(349,374)(350,375)(351,376)(352,373)(354,356)(357,368)(358,365)(359,366)(360,367)(362,364)(385,417)(386,420)(387,419)(388,418)(389,432)(390,429)(391,430)(392,431)(393,425)(394,428)(395,427)(396,426)(397,422)(398,423)(399,424)(400,421)(402,404)(405,416)(406,413)(407,414)(408,415)(410,412);
poly := sub<Sym(432)|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*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1, 
s2*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1*s0, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1 >;
References : None.
to this polytope

Twisty Puzzle