Polytope of Type {18,24} with group SmallGroup(1728,30258)

Overview

Group: SmallGroup(1728,30258)
Rank: 3
Schläfli Type: {18,24}
Vertices, edges, …: 36, 432, 48
Order of s₀s₁s₂: 18
Order of s₀s₁s₂s₁: 8
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Orientable

Quotients maximal quotients in bold

2-fold

{18,12}*864a

3-fold

4-fold

{18,12}*432c

6-fold

8-fold

{18,6}*216a

9-fold

{6,8}*192c

12-fold

18-fold

{6,4}*96

24-fold

36-fold

48-fold

{9,2}*36

72-fold

144-fold

216-fold

{2,2}*8

Covers minimal covers in bold

None in this atlas.

Irregular Quotients of which this is a minimal cover

Click an entry to reveal its facets and vertex figures.

P/N, where N=<(s0*s1)^6*(s0*s2*s1)^3> of order 2

24 facets

24 of {18}*36

18 vertex figures

18 of {24}*48

Representations

Permutation Representation (GAP)

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