Overview
- Group
- SmallGroup(1728,30272)
- Rank
- 3
- Schläfli Type
- {24,6}
- Vertices, edges, …
- 144, 432, 36
- Order of s0s1s2
- 6
- Order of s0s1s2s1
- 24
- Also known as
- if this polytope has a name.
Special Properties
- Compact Hyperbolic Quotient
- Locally Spherical
- Orientable
Quotients maximal quotients in bold
2-fold
3-fold
4-fold
6-fold
8-fold
9-fold
12-fold
16-fold
18-fold
24-fold
36-fold
72-fold
144-fold
216-fold
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*s0*s2)^2*s1*s2> of order 2
18 facets
- 18 of {24}*48
72 vertex figures
- 72 of {6}*12
P/N, where N=<s0*s1*s2*s1*s0*s2*(s1*s0)^2*(s2*s1)^2> of order 3
20 facets
48 vertex figures
- 48 of {6}*12
Representations
Permutation Representation (GAP)
s0 := ( 1,221)( 2,222)( 3,224)( 4,223)( 5,218)( 6,217)( 7,219)( 8,220)( 9,237)( 10,238)( 11,240)( 12,239)( 13,234)( 14,233)( 15,235)( 16,236)( 17,229)( 18,230)( 19,232)( 20,231)( 21,226)( 22,225)( 23,227)( 24,228)( 25,269)( 26,270)( 27,272)( 28,271)( 29,266)( 30,265)( 31,267)( 32,268)( 33,285)( 34,286)( 35,288)( 36,287)( 37,282)( 38,281)( 39,283)( 40,284)( 41,277)( 42,278)( 43,280)( 44,279)( 45,274)( 46,273)( 47,275)( 48,276)( 49,245)( 50,246)( 51,248)( 52,247)( 53,242)( 54,241)( 55,243)( 56,244)( 57,261)( 58,262)( 59,264)( 60,263)( 61,258)( 62,257)( 63,259)( 64,260)( 65,253)( 66,254)( 67,256)( 68,255)( 69,250)( 70,249)( 71,251)( 72,252)( 73,293)( 74,294)( 75,296)( 76,295)( 77,290)( 78,289)( 79,291)( 80,292)( 81,309)( 82,310)( 83,312)( 84,311)( 85,306)( 86,305)( 87,307)( 88,308)( 89,301)( 90,302)( 91,304)( 92,303)( 93,298)( 94,297)( 95,299)( 96,300)( 97,341)( 98,342)( 99,344)(100,343)(101,338)(102,337)(103,339)(104,340)(105,357)(106,358)(107,360)(108,359)(109,354)(110,353)(111,355)(112,356)(113,349)(114,350)(115,352)(116,351)(117,346)(118,345)(119,347)(120,348)(121,317)(122,318)(123,320)(124,319)(125,314)(126,313)(127,315)(128,316)(129,333)(130,334)(131,336)(132,335)(133,330)(134,329)(135,331)(136,332)(137,325)(138,326)(139,328)(140,327)(141,322)(142,321)(143,323)(144,324)(145,365)(146,366)(147,368)(148,367)(149,362)(150,361)(151,363)(152,364)(153,381)(154,382)(155,384)(156,383)(157,378)(158,377)(159,379)(160,380)(161,373)(162,374)(163,376)(164,375)(165,370)(166,369)(167,371)(168,372)(169,413)(170,414)(171,416)(172,415)(173,410)(174,409)(175,411)(176,412)(177,429)(178,430)(179,432)(180,431)(181,426)(182,425)(183,427)(184,428)(185,421)(186,422)(187,424)(188,423)(189,418)(190,417)(191,419)(192,420)(193,389)(194,390)(195,392)(196,391)(197,386)(198,385)(199,387)(200,388)(201,405)(202,406)(203,408)(204,407)(205,402)(206,401)(207,403)(208,404)(209,397)(210,398)(211,400)(212,399)(213,394)(214,393)(215,395)(216,396);; s1 := ( 1, 25)( 2, 26)( 3, 28)( 4, 27)( 5, 31)( 6, 32)( 7, 29)( 8, 30)( 9, 33)( 10, 34)( 11, 36)( 12, 35)( 13, 39)( 14, 40)( 15, 37)( 16, 38)( 17, 41)( 18, 42)( 19, 44)( 20, 43)( 21, 47)( 22, 48)( 23, 45)( 24, 46)( 51, 52)( 53, 55)( 54, 56)( 59, 60)( 61, 63)( 62, 64)( 67, 68)( 69, 71)( 70, 72)( 73,169)( 74,170)( 75,172)( 76,171)( 77,175)( 78,176)( 79,173)( 80,174)( 81,177)( 82,178)( 83,180)( 84,179)( 85,183)( 86,184)( 87,181)( 88,182)( 89,185)( 90,186)( 91,188)( 92,187)( 93,191)( 94,192)( 95,189)( 96,190)( 97,145)( 98,146)( 99,148)(100,147)(101,151)(102,152)(103,149)(104,150)(105,153)(106,154)(107,156)(108,155)(109,159)(110,160)(111,157)(112,158)(113,161)(114,162)(115,164)(116,163)(117,167)(118,168)(119,165)(120,166)(121,193)(122,194)(123,196)(124,195)(125,199)(126,200)(127,197)(128,198)(129,201)(130,202)(131,204)(132,203)(133,207)(134,208)(135,205)(136,206)(137,209)(138,210)(139,212)(140,211)(141,215)(142,216)(143,213)(144,214)(217,241)(218,242)(219,244)(220,243)(221,247)(222,248)(223,245)(224,246)(225,249)(226,250)(227,252)(228,251)(229,255)(230,256)(231,253)(232,254)(233,257)(234,258)(235,260)(236,259)(237,263)(238,264)(239,261)(240,262)(267,268)(269,271)(270,272)(275,276)(277,279)(278,280)(283,284)(285,287)(286,288)(289,385)(290,386)(291,388)(292,387)(293,391)(294,392)(295,389)(296,390)(297,393)(298,394)(299,396)(300,395)(301,399)(302,400)(303,397)(304,398)(305,401)(306,402)(307,404)(308,403)(309,407)(310,408)(311,405)(312,406)(313,361)(314,362)(315,364)(316,363)(317,367)(318,368)(319,365)(320,366)(321,369)(322,370)(323,372)(324,371)(325,375)(326,376)(327,373)(328,374)(329,377)(330,378)(331,380)(332,379)(333,383)(334,384)(335,381)(336,382)(337,409)(338,410)(339,412)(340,411)(341,415)(342,416)(343,413)(344,414)(345,417)(346,418)(347,420)(348,419)(349,423)(350,424)(351,421)(352,422)(353,425)(354,426)(355,428)(356,427)(357,431)(358,432)(359,429)(360,430);; s2 := ( 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)( 25,105)( 26,106)( 27,111)( 28,112)( 29,110)( 30,109)( 31,107)( 32,108)( 33, 97)( 34, 98)( 35,103)( 36,104)( 37,102)( 38,101)( 39, 99)( 40,100)( 41,113)( 42,114)( 43,119)( 44,120)( 45,118)( 46,117)( 47,115)( 48,116)( 49,137)( 50,138)( 51,143)( 52,144)( 53,142)( 54,141)( 55,139)( 56,140)( 57,129)( 58,130)( 59,135)( 60,136)( 61,134)( 62,133)( 63,131)( 64,132)( 65,121)( 66,122)( 67,127)( 68,128)( 69,126)( 70,125)( 71,123)( 72,124)(147,151)(148,152)(149,150)(153,161)(154,162)(155,167)(156,168)(157,166)(158,165)(159,163)(160,164)(169,177)(170,178)(171,183)(172,184)(173,182)(174,181)(175,179)(176,180)(187,191)(188,192)(189,190)(193,209)(194,210)(195,215)(196,216)(197,214)(198,213)(199,211)(200,212)(203,207)(204,208)(205,206)(217,290)(218,289)(219,296)(220,295)(221,293)(222,294)(223,292)(224,291)(225,306)(226,305)(227,312)(228,311)(229,309)(230,310)(231,308)(232,307)(233,298)(234,297)(235,304)(236,303)(237,301)(238,302)(239,300)(240,299)(241,322)(242,321)(243,328)(244,327)(245,325)(246,326)(247,324)(248,323)(249,314)(250,313)(251,320)(252,319)(253,317)(254,318)(255,316)(256,315)(257,330)(258,329)(259,336)(260,335)(261,333)(262,334)(263,332)(264,331)(265,354)(266,353)(267,360)(268,359)(269,357)(270,358)(271,356)(272,355)(273,346)(274,345)(275,352)(276,351)(277,349)(278,350)(279,348)(280,347)(281,338)(282,337)(283,344)(284,343)(285,341)(286,342)(287,340)(288,339)(361,362)(363,368)(364,367)(369,378)(370,377)(371,384)(372,383)(373,381)(374,382)(375,380)(376,379)(385,394)(386,393)(387,400)(388,399)(389,397)(390,398)(391,396)(392,395)(401,402)(403,408)(404,407)(409,426)(410,425)(411,432)(412,431)(413,429)(414,430)(415,428)(416,427)(417,418)(419,424)(420,423);; 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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(432)!( 1,221)( 2,222)( 3,224)( 4,223)( 5,218)( 6,217)( 7,219)( 8,220)( 9,237)( 10,238)( 11,240)( 12,239)( 13,234)( 14,233)( 15,235)( 16,236)( 17,229)( 18,230)( 19,232)( 20,231)( 21,226)( 22,225)( 23,227)( 24,228)( 25,269)( 26,270)( 27,272)( 28,271)( 29,266)( 30,265)( 31,267)( 32,268)( 33,285)( 34,286)( 35,288)( 36,287)( 37,282)( 38,281)( 39,283)( 40,284)( 41,277)( 42,278)( 43,280)( 44,279)( 45,274)( 46,273)( 47,275)( 48,276)( 49,245)( 50,246)( 51,248)( 52,247)( 53,242)( 54,241)( 55,243)( 56,244)( 57,261)( 58,262)( 59,264)( 60,263)( 61,258)( 62,257)( 63,259)( 64,260)( 65,253)( 66,254)( 67,256)( 68,255)( 69,250)( 70,249)( 71,251)( 72,252)( 73,293)( 74,294)( 75,296)( 76,295)( 77,290)( 78,289)( 79,291)( 80,292)( 81,309)( 82,310)( 83,312)( 84,311)( 85,306)( 86,305)( 87,307)( 88,308)( 89,301)( 90,302)( 91,304)( 92,303)( 93,298)( 94,297)( 95,299)( 96,300)( 97,341)( 98,342)( 99,344)(100,343)(101,338)(102,337)(103,339)(104,340)(105,357)(106,358)(107,360)(108,359)(109,354)(110,353)(111,355)(112,356)(113,349)(114,350)(115,352)(116,351)(117,346)(118,345)(119,347)(120,348)(121,317)(122,318)(123,320)(124,319)(125,314)(126,313)(127,315)(128,316)(129,333)(130,334)(131,336)(132,335)(133,330)(134,329)(135,331)(136,332)(137,325)(138,326)(139,328)(140,327)(141,322)(142,321)(143,323)(144,324)(145,365)(146,366)(147,368)(148,367)(149,362)(150,361)(151,363)(152,364)(153,381)(154,382)(155,384)(156,383)(157,378)(158,377)(159,379)(160,380)(161,373)(162,374)(163,376)(164,375)(165,370)(166,369)(167,371)(168,372)(169,413)(170,414)(171,416)(172,415)(173,410)(174,409)(175,411)(176,412)(177,429)(178,430)(179,432)(180,431)(181,426)(182,425)(183,427)(184,428)(185,421)(186,422)(187,424)(188,423)(189,418)(190,417)(191,419)(192,420)(193,389)(194,390)(195,392)(196,391)(197,386)(198,385)(199,387)(200,388)(201,405)(202,406)(203,408)(204,407)(205,402)(206,401)(207,403)(208,404)(209,397)(210,398)(211,400)(212,399)(213,394)(214,393)(215,395)(216,396); s1 := Sym(432)!( 1, 25)( 2, 26)( 3, 28)( 4, 27)( 5, 31)( 6, 32)( 7, 29)( 8, 30)( 9, 33)( 10, 34)( 11, 36)( 12, 35)( 13, 39)( 14, 40)( 15, 37)( 16, 38)( 17, 41)( 18, 42)( 19, 44)( 20, 43)( 21, 47)( 22, 48)( 23, 45)( 24, 46)( 51, 52)( 53, 55)( 54, 56)( 59, 60)( 61, 63)( 62, 64)( 67, 68)( 69, 71)( 70, 72)( 73,169)( 74,170)( 75,172)( 76,171)( 77,175)( 78,176)( 79,173)( 80,174)( 81,177)( 82,178)( 83,180)( 84,179)( 85,183)( 86,184)( 87,181)( 88,182)( 89,185)( 90,186)( 91,188)( 92,187)( 93,191)( 94,192)( 95,189)( 96,190)( 97,145)( 98,146)( 99,148)(100,147)(101,151)(102,152)(103,149)(104,150)(105,153)(106,154)(107,156)(108,155)(109,159)(110,160)(111,157)(112,158)(113,161)(114,162)(115,164)(116,163)(117,167)(118,168)(119,165)(120,166)(121,193)(122,194)(123,196)(124,195)(125,199)(126,200)(127,197)(128,198)(129,201)(130,202)(131,204)(132,203)(133,207)(134,208)(135,205)(136,206)(137,209)(138,210)(139,212)(140,211)(141,215)(142,216)(143,213)(144,214)(217,241)(218,242)(219,244)(220,243)(221,247)(222,248)(223,245)(224,246)(225,249)(226,250)(227,252)(228,251)(229,255)(230,256)(231,253)(232,254)(233,257)(234,258)(235,260)(236,259)(237,263)(238,264)(239,261)(240,262)(267,268)(269,271)(270,272)(275,276)(277,279)(278,280)(283,284)(285,287)(286,288)(289,385)(290,386)(291,388)(292,387)(293,391)(294,392)(295,389)(296,390)(297,393)(298,394)(299,396)(300,395)(301,399)(302,400)(303,397)(304,398)(305,401)(306,402)(307,404)(308,403)(309,407)(310,408)(311,405)(312,406)(313,361)(314,362)(315,364)(316,363)(317,367)(318,368)(319,365)(320,366)(321,369)(322,370)(323,372)(324,371)(325,375)(326,376)(327,373)(328,374)(329,377)(330,378)(331,380)(332,379)(333,383)(334,384)(335,381)(336,382)(337,409)(338,410)(339,412)(340,411)(341,415)(342,416)(343,413)(344,414)(345,417)(346,418)(347,420)(348,419)(349,423)(350,424)(351,421)(352,422)(353,425)(354,426)(355,428)(356,427)(357,431)(358,432)(359,429)(360,430); s2 := 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)( 25,105)( 26,106)( 27,111)( 28,112)( 29,110)( 30,109)( 31,107)( 32,108)( 33, 97)( 34, 98)( 35,103)( 36,104)( 37,102)( 38,101)( 39, 99)( 40,100)( 41,113)( 42,114)( 43,119)( 44,120)( 45,118)( 46,117)( 47,115)( 48,116)( 49,137)( 50,138)( 51,143)( 52,144)( 53,142)( 54,141)( 55,139)( 56,140)( 57,129)( 58,130)( 59,135)( 60,136)( 61,134)( 62,133)( 63,131)( 64,132)( 65,121)( 66,122)( 67,127)( 68,128)( 69,126)( 70,125)( 71,123)( 72,124)(147,151)(148,152)(149,150)(153,161)(154,162)(155,167)(156,168)(157,166)(158,165)(159,163)(160,164)(169,177)(170,178)(171,183)(172,184)(173,182)(174,181)(175,179)(176,180)(187,191)(188,192)(189,190)(193,209)(194,210)(195,215)(196,216)(197,214)(198,213)(199,211)(200,212)(203,207)(204,208)(205,206)(217,290)(218,289)(219,296)(220,295)(221,293)(222,294)(223,292)(224,291)(225,306)(226,305)(227,312)(228,311)(229,309)(230,310)(231,308)(232,307)(233,298)(234,297)(235,304)(236,303)(237,301)(238,302)(239,300)(240,299)(241,322)(242,321)(243,328)(244,327)(245,325)(246,326)(247,324)(248,323)(249,314)(250,313)(251,320)(252,319)(253,317)(254,318)(255,316)(256,315)(257,330)(258,329)(259,336)(260,335)(261,333)(262,334)(263,332)(264,331)(265,354)(266,353)(267,360)(268,359)(269,357)(270,358)(271,356)(272,355)(273,346)(274,345)(275,352)(276,351)(277,349)(278,350)(279,348)(280,347)(281,338)(282,337)(283,344)(284,343)(285,341)(286,342)(287,340)(288,339)(361,362)(363,368)(364,367)(369,378)(370,377)(371,384)(372,383)(373,381)(374,382)(375,380)(376,379)(385,394)(386,393)(387,400)(388,399)(389,397)(390,398)(391,396)(392,395)(401,402)(403,408)(404,407)(409,426)(410,425)(411,432)(412,431)(413,429)(414,430)(415,428)(416,427)(417,418)(419,424)(420,423); 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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s0*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1 >;
References
None.
to this polytope.