Overview
- Group
- SmallGroup(1728,3359)
- Rank
- 3
- Schläfli Type
- {24,36}
- Vertices, edges, …
- 24, 432, 36
- Order of s0s1s2
- 72
- Order of s0s1s2s1
- 12
- Also known as
- if this polytope has a name.
Special Properties
- Compact Hyperbolic Quotient
- Locally Spherical
- Orientable
- Flat
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
27-fold
36-fold
48-fold
54-fold
72-fold
108-fold
144-fold
216-fold
Covers minimal covers in bold
None in this atlas.
Irregular Quotients of which this is a minimal cover
None.
Representations
Permutation Representation (GAP)
s0 := ( 4, 7)( 5, 8)( 6, 9)( 13, 16)( 14, 17)( 15, 18)( 22, 25)( 23, 26)( 24, 27)( 31, 34)( 32, 35)( 33, 36)( 40, 43)( 41, 44)( 42, 45)( 49, 52)( 50, 53)( 51, 54)( 58, 61)( 59, 62)( 60, 63)( 67, 70)( 68, 71)( 69, 72)( 76, 79)( 77, 80)( 78, 81)( 85, 88)( 86, 89)( 87, 90)( 94, 97)( 95, 98)( 96, 99)(103,106)(104,107)(105,108)(109,136)(110,137)(111,138)(112,142)(113,143)(114,144)(115,139)(116,140)(117,141)(118,145)(119,146)(120,147)(121,151)(122,152)(123,153)(124,148)(125,149)(126,150)(127,154)(128,155)(129,156)(130,160)(131,161)(132,162)(133,157)(134,158)(135,159)(163,190)(164,191)(165,192)(166,196)(167,197)(168,198)(169,193)(170,194)(171,195)(172,199)(173,200)(174,201)(175,205)(176,206)(177,207)(178,202)(179,203)(180,204)(181,208)(182,209)(183,210)(184,214)(185,215)(186,216)(187,211)(188,212)(189,213)(217,325)(218,326)(219,327)(220,331)(221,332)(222,333)(223,328)(224,329)(225,330)(226,334)(227,335)(228,336)(229,340)(230,341)(231,342)(232,337)(233,338)(234,339)(235,343)(236,344)(237,345)(238,349)(239,350)(240,351)(241,346)(242,347)(243,348)(244,352)(245,353)(246,354)(247,358)(248,359)(249,360)(250,355)(251,356)(252,357)(253,361)(254,362)(255,363)(256,367)(257,368)(258,369)(259,364)(260,365)(261,366)(262,370)(263,371)(264,372)(265,376)(266,377)(267,378)(268,373)(269,374)(270,375)(271,379)(272,380)(273,381)(274,385)(275,386)(276,387)(277,382)(278,383)(279,384)(280,388)(281,389)(282,390)(283,394)(284,395)(285,396)(286,391)(287,392)(288,393)(289,397)(290,398)(291,399)(292,403)(293,404)(294,405)(295,400)(296,401)(297,402)(298,406)(299,407)(300,408)(301,412)(302,413)(303,414)(304,409)(305,410)(306,411)(307,415)(308,416)(309,417)(310,421)(311,422)(312,423)(313,418)(314,419)(315,420)(316,424)(317,425)(318,426)(319,430)(320,431)(321,432)(322,427)(323,428)(324,429);; s1 := ( 1,220)( 2,222)( 3,221)( 4,217)( 5,219)( 6,218)( 7,223)( 8,225)( 9,224)( 10,240)( 11,239)( 12,238)( 13,237)( 14,236)( 15,235)( 16,243)( 17,242)( 18,241)( 19,231)( 20,230)( 21,229)( 22,228)( 23,227)( 24,226)( 25,234)( 26,233)( 27,232)( 28,247)( 29,249)( 30,248)( 31,244)( 32,246)( 33,245)( 34,250)( 35,252)( 36,251)( 37,267)( 38,266)( 39,265)( 40,264)( 41,263)( 42,262)( 43,270)( 44,269)( 45,268)( 46,258)( 47,257)( 48,256)( 49,255)( 50,254)( 51,253)( 52,261)( 53,260)( 54,259)( 55,301)( 56,303)( 57,302)( 58,298)( 59,300)( 60,299)( 61,304)( 62,306)( 63,305)( 64,321)( 65,320)( 66,319)( 67,318)( 68,317)( 69,316)( 70,324)( 71,323)( 72,322)( 73,312)( 74,311)( 75,310)( 76,309)( 77,308)( 78,307)( 79,315)( 80,314)( 81,313)( 82,274)( 83,276)( 84,275)( 85,271)( 86,273)( 87,272)( 88,277)( 89,279)( 90,278)( 91,294)( 92,293)( 93,292)( 94,291)( 95,290)( 96,289)( 97,297)( 98,296)( 99,295)(100,285)(101,284)(102,283)(103,282)(104,281)(105,280)(106,288)(107,287)(108,286)(109,355)(110,357)(111,356)(112,352)(113,354)(114,353)(115,358)(116,360)(117,359)(118,375)(119,374)(120,373)(121,372)(122,371)(123,370)(124,378)(125,377)(126,376)(127,366)(128,365)(129,364)(130,363)(131,362)(132,361)(133,369)(134,368)(135,367)(136,328)(137,330)(138,329)(139,325)(140,327)(141,326)(142,331)(143,333)(144,332)(145,348)(146,347)(147,346)(148,345)(149,344)(150,343)(151,351)(152,350)(153,349)(154,339)(155,338)(156,337)(157,336)(158,335)(159,334)(160,342)(161,341)(162,340)(163,382)(164,384)(165,383)(166,379)(167,381)(168,380)(169,385)(170,387)(171,386)(172,402)(173,401)(174,400)(175,399)(176,398)(177,397)(178,405)(179,404)(180,403)(181,393)(182,392)(183,391)(184,390)(185,389)(186,388)(187,396)(188,395)(189,394)(190,409)(191,411)(192,410)(193,406)(194,408)(195,407)(196,412)(197,414)(198,413)(199,429)(200,428)(201,427)(202,426)(203,425)(204,424)(205,432)(206,431)(207,430)(208,420)(209,419)(210,418)(211,417)(212,416)(213,415)(214,423)(215,422)(216,421);; s2 := ( 1, 10)( 2, 12)( 3, 11)( 4, 16)( 5, 18)( 6, 17)( 7, 13)( 8, 15)( 9, 14)( 19, 21)( 22, 27)( 23, 26)( 24, 25)( 28, 37)( 29, 39)( 30, 38)( 31, 43)( 32, 45)( 33, 44)( 34, 40)( 35, 42)( 36, 41)( 46, 48)( 49, 54)( 50, 53)( 51, 52)( 55, 91)( 56, 93)( 57, 92)( 58, 97)( 59, 99)( 60, 98)( 61, 94)( 62, 96)( 63, 95)( 64, 82)( 65, 84)( 66, 83)( 67, 88)( 68, 90)( 69, 89)( 70, 85)( 71, 87)( 72, 86)( 73,102)( 74,101)( 75,100)( 76,108)( 77,107)( 78,106)( 79,105)( 80,104)( 81,103)(109,145)(110,147)(111,146)(112,151)(113,153)(114,152)(115,148)(116,150)(117,149)(118,136)(119,138)(120,137)(121,142)(122,144)(123,143)(124,139)(125,141)(126,140)(127,156)(128,155)(129,154)(130,162)(131,161)(132,160)(133,159)(134,158)(135,157)(163,172)(164,174)(165,173)(166,178)(167,180)(168,179)(169,175)(170,177)(171,176)(181,183)(184,189)(185,188)(186,187)(190,199)(191,201)(192,200)(193,205)(194,207)(195,206)(196,202)(197,204)(198,203)(208,210)(211,216)(212,215)(213,214)(217,388)(218,390)(219,389)(220,394)(221,396)(222,395)(223,391)(224,393)(225,392)(226,379)(227,381)(228,380)(229,385)(230,387)(231,386)(232,382)(233,384)(234,383)(235,399)(236,398)(237,397)(238,405)(239,404)(240,403)(241,402)(242,401)(243,400)(244,415)(245,417)(246,416)(247,421)(248,423)(249,422)(250,418)(251,420)(252,419)(253,406)(254,408)(255,407)(256,412)(257,414)(258,413)(259,409)(260,411)(261,410)(262,426)(263,425)(264,424)(265,432)(266,431)(267,430)(268,429)(269,428)(270,427)(271,334)(272,336)(273,335)(274,340)(275,342)(276,341)(277,337)(278,339)(279,338)(280,325)(281,327)(282,326)(283,331)(284,333)(285,332)(286,328)(287,330)(288,329)(289,345)(290,344)(291,343)(292,351)(293,350)(294,349)(295,348)(296,347)(297,346)(298,361)(299,363)(300,362)(301,367)(302,369)(303,368)(304,364)(305,366)(306,365)(307,352)(308,354)(309,353)(310,358)(311,360)(312,359)(313,355)(314,357)(315,356)(316,372)(317,371)(318,370)(319,378)(320,377)(321,376)(322,375)(323,374)(324,373);; 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*s0*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,
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*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 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(432)!( 4, 7)( 5, 8)( 6, 9)( 13, 16)( 14, 17)( 15, 18)( 22, 25)( 23, 26)( 24, 27)( 31, 34)( 32, 35)( 33, 36)( 40, 43)( 41, 44)( 42, 45)( 49, 52)( 50, 53)( 51, 54)( 58, 61)( 59, 62)( 60, 63)( 67, 70)( 68, 71)( 69, 72)( 76, 79)( 77, 80)( 78, 81)( 85, 88)( 86, 89)( 87, 90)( 94, 97)( 95, 98)( 96, 99)(103,106)(104,107)(105,108)(109,136)(110,137)(111,138)(112,142)(113,143)(114,144)(115,139)(116,140)(117,141)(118,145)(119,146)(120,147)(121,151)(122,152)(123,153)(124,148)(125,149)(126,150)(127,154)(128,155)(129,156)(130,160)(131,161)(132,162)(133,157)(134,158)(135,159)(163,190)(164,191)(165,192)(166,196)(167,197)(168,198)(169,193)(170,194)(171,195)(172,199)(173,200)(174,201)(175,205)(176,206)(177,207)(178,202)(179,203)(180,204)(181,208)(182,209)(183,210)(184,214)(185,215)(186,216)(187,211)(188,212)(189,213)(217,325)(218,326)(219,327)(220,331)(221,332)(222,333)(223,328)(224,329)(225,330)(226,334)(227,335)(228,336)(229,340)(230,341)(231,342)(232,337)(233,338)(234,339)(235,343)(236,344)(237,345)(238,349)(239,350)(240,351)(241,346)(242,347)(243,348)(244,352)(245,353)(246,354)(247,358)(248,359)(249,360)(250,355)(251,356)(252,357)(253,361)(254,362)(255,363)(256,367)(257,368)(258,369)(259,364)(260,365)(261,366)(262,370)(263,371)(264,372)(265,376)(266,377)(267,378)(268,373)(269,374)(270,375)(271,379)(272,380)(273,381)(274,385)(275,386)(276,387)(277,382)(278,383)(279,384)(280,388)(281,389)(282,390)(283,394)(284,395)(285,396)(286,391)(287,392)(288,393)(289,397)(290,398)(291,399)(292,403)(293,404)(294,405)(295,400)(296,401)(297,402)(298,406)(299,407)(300,408)(301,412)(302,413)(303,414)(304,409)(305,410)(306,411)(307,415)(308,416)(309,417)(310,421)(311,422)(312,423)(313,418)(314,419)(315,420)(316,424)(317,425)(318,426)(319,430)(320,431)(321,432)(322,427)(323,428)(324,429); s1 := Sym(432)!( 1,220)( 2,222)( 3,221)( 4,217)( 5,219)( 6,218)( 7,223)( 8,225)( 9,224)( 10,240)( 11,239)( 12,238)( 13,237)( 14,236)( 15,235)( 16,243)( 17,242)( 18,241)( 19,231)( 20,230)( 21,229)( 22,228)( 23,227)( 24,226)( 25,234)( 26,233)( 27,232)( 28,247)( 29,249)( 30,248)( 31,244)( 32,246)( 33,245)( 34,250)( 35,252)( 36,251)( 37,267)( 38,266)( 39,265)( 40,264)( 41,263)( 42,262)( 43,270)( 44,269)( 45,268)( 46,258)( 47,257)( 48,256)( 49,255)( 50,254)( 51,253)( 52,261)( 53,260)( 54,259)( 55,301)( 56,303)( 57,302)( 58,298)( 59,300)( 60,299)( 61,304)( 62,306)( 63,305)( 64,321)( 65,320)( 66,319)( 67,318)( 68,317)( 69,316)( 70,324)( 71,323)( 72,322)( 73,312)( 74,311)( 75,310)( 76,309)( 77,308)( 78,307)( 79,315)( 80,314)( 81,313)( 82,274)( 83,276)( 84,275)( 85,271)( 86,273)( 87,272)( 88,277)( 89,279)( 90,278)( 91,294)( 92,293)( 93,292)( 94,291)( 95,290)( 96,289)( 97,297)( 98,296)( 99,295)(100,285)(101,284)(102,283)(103,282)(104,281)(105,280)(106,288)(107,287)(108,286)(109,355)(110,357)(111,356)(112,352)(113,354)(114,353)(115,358)(116,360)(117,359)(118,375)(119,374)(120,373)(121,372)(122,371)(123,370)(124,378)(125,377)(126,376)(127,366)(128,365)(129,364)(130,363)(131,362)(132,361)(133,369)(134,368)(135,367)(136,328)(137,330)(138,329)(139,325)(140,327)(141,326)(142,331)(143,333)(144,332)(145,348)(146,347)(147,346)(148,345)(149,344)(150,343)(151,351)(152,350)(153,349)(154,339)(155,338)(156,337)(157,336)(158,335)(159,334)(160,342)(161,341)(162,340)(163,382)(164,384)(165,383)(166,379)(167,381)(168,380)(169,385)(170,387)(171,386)(172,402)(173,401)(174,400)(175,399)(176,398)(177,397)(178,405)(179,404)(180,403)(181,393)(182,392)(183,391)(184,390)(185,389)(186,388)(187,396)(188,395)(189,394)(190,409)(191,411)(192,410)(193,406)(194,408)(195,407)(196,412)(197,414)(198,413)(199,429)(200,428)(201,427)(202,426)(203,425)(204,424)(205,432)(206,431)(207,430)(208,420)(209,419)(210,418)(211,417)(212,416)(213,415)(214,423)(215,422)(216,421); s2 := Sym(432)!( 1, 10)( 2, 12)( 3, 11)( 4, 16)( 5, 18)( 6, 17)( 7, 13)( 8, 15)( 9, 14)( 19, 21)( 22, 27)( 23, 26)( 24, 25)( 28, 37)( 29, 39)( 30, 38)( 31, 43)( 32, 45)( 33, 44)( 34, 40)( 35, 42)( 36, 41)( 46, 48)( 49, 54)( 50, 53)( 51, 52)( 55, 91)( 56, 93)( 57, 92)( 58, 97)( 59, 99)( 60, 98)( 61, 94)( 62, 96)( 63, 95)( 64, 82)( 65, 84)( 66, 83)( 67, 88)( 68, 90)( 69, 89)( 70, 85)( 71, 87)( 72, 86)( 73,102)( 74,101)( 75,100)( 76,108)( 77,107)( 78,106)( 79,105)( 80,104)( 81,103)(109,145)(110,147)(111,146)(112,151)(113,153)(114,152)(115,148)(116,150)(117,149)(118,136)(119,138)(120,137)(121,142)(122,144)(123,143)(124,139)(125,141)(126,140)(127,156)(128,155)(129,154)(130,162)(131,161)(132,160)(133,159)(134,158)(135,157)(163,172)(164,174)(165,173)(166,178)(167,180)(168,179)(169,175)(170,177)(171,176)(181,183)(184,189)(185,188)(186,187)(190,199)(191,201)(192,200)(193,205)(194,207)(195,206)(196,202)(197,204)(198,203)(208,210)(211,216)(212,215)(213,214)(217,388)(218,390)(219,389)(220,394)(221,396)(222,395)(223,391)(224,393)(225,392)(226,379)(227,381)(228,380)(229,385)(230,387)(231,386)(232,382)(233,384)(234,383)(235,399)(236,398)(237,397)(238,405)(239,404)(240,403)(241,402)(242,401)(243,400)(244,415)(245,417)(246,416)(247,421)(248,423)(249,422)(250,418)(251,420)(252,419)(253,406)(254,408)(255,407)(256,412)(257,414)(258,413)(259,409)(260,411)(261,410)(262,426)(263,425)(264,424)(265,432)(266,431)(267,430)(268,429)(269,428)(270,427)(271,334)(272,336)(273,335)(274,340)(275,342)(276,341)(277,337)(278,339)(279,338)(280,325)(281,327)(282,326)(283,331)(284,333)(285,332)(286,328)(287,330)(288,329)(289,345)(290,344)(291,343)(292,351)(293,350)(294,349)(295,348)(296,347)(297,346)(298,361)(299,363)(300,362)(301,367)(302,369)(303,368)(304,364)(305,366)(306,365)(307,352)(308,354)(309,353)(310,358)(311,360)(312,359)(313,355)(314,357)(315,356)(316,372)(317,371)(318,370)(319,378)(320,377)(321,376)(322,375)(323,374)(324,373); 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*s0*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, 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*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 >;
References
None.
to this polytope.