Overview
- Group
- SmallGroup(1728,30201)
- Rank
- 3
- Schläfli Type
- {6,36}
- Vertices, edges, …
- 24, 432, 144
- 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
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
48-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.
Representations
Permutation Representation (GAP)
s0 := ( 3, 4)( 5, 7)( 6, 8)( 11, 12)( 13, 15)( 14, 16)( 19, 20)( 21, 23)( 22, 24)( 27, 28)( 29, 31)( 30, 32)( 35, 36)( 37, 39)( 38, 40)( 43, 44)( 45, 47)( 46, 48)( 51, 52)( 53, 55)( 54, 56)( 59, 60)( 61, 63)( 62, 64)( 67, 68)( 69, 71)( 70, 72)( 73,145)( 74,146)( 75,148)( 76,147)( 77,151)( 78,152)( 79,149)( 80,150)( 81,153)( 82,154)( 83,156)( 84,155)( 85,159)( 86,160)( 87,157)( 88,158)( 89,161)( 90,162)( 91,164)( 92,163)( 93,167)( 94,168)( 95,165)( 96,166)( 97,169)( 98,170)( 99,172)(100,171)(101,175)(102,176)(103,173)(104,174)(105,177)(106,178)(107,180)(108,179)(109,183)(110,184)(111,181)(112,182)(113,185)(114,186)(115,188)(116,187)(117,191)(118,192)(119,189)(120,190)(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)(217,218)(221,224)(222,223)(225,226)(229,232)(230,231)(233,234)(237,240)(238,239)(241,242)(245,248)(246,247)(249,250)(253,256)(254,255)(257,258)(261,264)(262,263)(265,266)(269,272)(270,271)(273,274)(277,280)(278,279)(281,282)(285,288)(286,287)(289,362)(290,361)(291,363)(292,364)(293,368)(294,367)(295,366)(296,365)(297,370)(298,369)(299,371)(300,372)(301,376)(302,375)(303,374)(304,373)(305,378)(306,377)(307,379)(308,380)(309,384)(310,383)(311,382)(312,381)(313,386)(314,385)(315,387)(316,388)(317,392)(318,391)(319,390)(320,389)(321,394)(322,393)(323,395)(324,396)(325,400)(326,399)(327,398)(328,397)(329,402)(330,401)(331,403)(332,404)(333,408)(334,407)(335,406)(336,405)(337,410)(338,409)(339,411)(340,412)(341,416)(342,415)(343,414)(344,413)(345,418)(346,417)(347,419)(348,420)(349,424)(350,423)(351,422)(352,421)(353,426)(354,425)(355,427)(356,428)(357,432)(358,431)(359,430)(360,429);; 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)( 25,137)( 26,138)( 27,143)( 28,144)( 29,142)( 30,141)( 31,139)( 32,140)( 33,129)( 34,130)( 35,135)( 36,136)( 37,134)( 38,133)( 39,131)( 40,132)( 41,121)( 42,122)( 43,127)( 44,128)( 45,126)( 46,125)( 47,123)( 48,124)( 49,113)( 50,114)( 51,119)( 52,120)( 53,118)( 54,117)( 55,115)( 56,116)( 57,105)( 58,106)( 59,111)( 60,112)( 61,110)( 62,109)( 63,107)( 64,108)( 65, 97)( 66, 98)( 67,103)( 68,104)( 69,102)( 70,101)( 71, 99)( 72,100)(147,151)(148,152)(149,150)(153,161)(154,162)(155,167)(156,168)(157,166)(158,165)(159,163)(160,164)(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)(217,290)(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)(241,354)(242,353)(243,360)(244,359)(245,357)(246,358)(247,356)(248,355)(249,346)(250,345)(251,352)(252,351)(253,349)(254,350)(255,348)(256,347)(257,338)(258,337)(259,344)(260,343)(261,341)(262,342)(263,340)(264,339)(265,330)(266,329)(267,336)(268,335)(269,333)(270,334)(271,332)(272,331)(273,322)(274,321)(275,328)(276,327)(277,325)(278,326)(279,324)(280,323)(281,314)(282,313)(283,320)(284,319)(285,317)(286,318)(287,316)(288,315)(361,362)(363,368)(364,367)(369,378)(370,377)(371,384)(372,383)(373,381)(374,382)(375,380)(376,379)(385,426)(386,425)(387,432)(388,431)(389,429)(390,430)(391,428)(392,427)(393,418)(394,417)(395,424)(396,423)(397,421)(398,422)(399,420)(400,419)(401,410)(402,409)(403,416)(404,415)(405,413)(406,414)(407,412)(408,411);; s2 := ( 1,243)( 2,244)( 3,241)( 4,242)( 5,246)( 6,245)( 7,247)( 8,248)( 9,259)( 10,260)( 11,257)( 12,258)( 13,262)( 14,261)( 15,263)( 16,264)( 17,251)( 18,252)( 19,249)( 20,250)( 21,254)( 22,253)( 23,255)( 24,256)( 25,219)( 26,220)( 27,217)( 28,218)( 29,222)( 30,221)( 31,223)( 32,224)( 33,235)( 34,236)( 35,233)( 36,234)( 37,238)( 38,237)( 39,239)( 40,240)( 41,227)( 42,228)( 43,225)( 44,226)( 45,230)( 46,229)( 47,231)( 48,232)( 49,283)( 50,284)( 51,281)( 52,282)( 53,286)( 54,285)( 55,287)( 56,288)( 57,275)( 58,276)( 59,273)( 60,274)( 61,278)( 62,277)( 63,279)( 64,280)( 65,267)( 66,268)( 67,265)( 68,266)( 69,270)( 70,269)( 71,271)( 72,272)( 73,387)( 74,388)( 75,385)( 76,386)( 77,390)( 78,389)( 79,391)( 80,392)( 81,403)( 82,404)( 83,401)( 84,402)( 85,406)( 86,405)( 87,407)( 88,408)( 89,395)( 90,396)( 91,393)( 92,394)( 93,398)( 94,397)( 95,399)( 96,400)( 97,363)( 98,364)( 99,361)(100,362)(101,366)(102,365)(103,367)(104,368)(105,379)(106,380)(107,377)(108,378)(109,382)(110,381)(111,383)(112,384)(113,371)(114,372)(115,369)(116,370)(117,374)(118,373)(119,375)(120,376)(121,427)(122,428)(123,425)(124,426)(125,430)(126,429)(127,431)(128,432)(129,419)(130,420)(131,417)(132,418)(133,422)(134,421)(135,423)(136,424)(137,411)(138,412)(139,409)(140,410)(141,414)(142,413)(143,415)(144,416)(145,315)(146,316)(147,313)(148,314)(149,318)(150,317)(151,319)(152,320)(153,331)(154,332)(155,329)(156,330)(157,334)(158,333)(159,335)(160,336)(161,323)(162,324)(163,321)(164,322)(165,326)(166,325)(167,327)(168,328)(169,291)(170,292)(171,289)(172,290)(173,294)(174,293)(175,295)(176,296)(177,307)(178,308)(179,305)(180,306)(181,310)(182,309)(183,311)(184,312)(185,299)(186,300)(187,297)(188,298)(189,302)(190,301)(191,303)(192,304)(193,355)(194,356)(195,353)(196,354)(197,358)(198,357)(199,359)(200,360)(201,347)(202,348)(203,345)(204,346)(205,350)(206,349)(207,351)(208,352)(209,339)(210,340)(211,337)(212,338)(213,342)(214,341)(215,343)(216,344);; 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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s2*s1*s2*s0*s1*s0*s1*s2*s1*s2*s1*s2*s0*s1,
s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s2*s1*s0,
s2*s1*s0*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*s0*s2*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(432)!( 3, 4)( 5, 7)( 6, 8)( 11, 12)( 13, 15)( 14, 16)( 19, 20)( 21, 23)( 22, 24)( 27, 28)( 29, 31)( 30, 32)( 35, 36)( 37, 39)( 38, 40)( 43, 44)( 45, 47)( 46, 48)( 51, 52)( 53, 55)( 54, 56)( 59, 60)( 61, 63)( 62, 64)( 67, 68)( 69, 71)( 70, 72)( 73,145)( 74,146)( 75,148)( 76,147)( 77,151)( 78,152)( 79,149)( 80,150)( 81,153)( 82,154)( 83,156)( 84,155)( 85,159)( 86,160)( 87,157)( 88,158)( 89,161)( 90,162)( 91,164)( 92,163)( 93,167)( 94,168)( 95,165)( 96,166)( 97,169)( 98,170)( 99,172)(100,171)(101,175)(102,176)(103,173)(104,174)(105,177)(106,178)(107,180)(108,179)(109,183)(110,184)(111,181)(112,182)(113,185)(114,186)(115,188)(116,187)(117,191)(118,192)(119,189)(120,190)(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)(217,218)(221,224)(222,223)(225,226)(229,232)(230,231)(233,234)(237,240)(238,239)(241,242)(245,248)(246,247)(249,250)(253,256)(254,255)(257,258)(261,264)(262,263)(265,266)(269,272)(270,271)(273,274)(277,280)(278,279)(281,282)(285,288)(286,287)(289,362)(290,361)(291,363)(292,364)(293,368)(294,367)(295,366)(296,365)(297,370)(298,369)(299,371)(300,372)(301,376)(302,375)(303,374)(304,373)(305,378)(306,377)(307,379)(308,380)(309,384)(310,383)(311,382)(312,381)(313,386)(314,385)(315,387)(316,388)(317,392)(318,391)(319,390)(320,389)(321,394)(322,393)(323,395)(324,396)(325,400)(326,399)(327,398)(328,397)(329,402)(330,401)(331,403)(332,404)(333,408)(334,407)(335,406)(336,405)(337,410)(338,409)(339,411)(340,412)(341,416)(342,415)(343,414)(344,413)(345,418)(346,417)(347,419)(348,420)(349,424)(350,423)(351,422)(352,421)(353,426)(354,425)(355,427)(356,428)(357,432)(358,431)(359,430)(360,429); 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)( 25,137)( 26,138)( 27,143)( 28,144)( 29,142)( 30,141)( 31,139)( 32,140)( 33,129)( 34,130)( 35,135)( 36,136)( 37,134)( 38,133)( 39,131)( 40,132)( 41,121)( 42,122)( 43,127)( 44,128)( 45,126)( 46,125)( 47,123)( 48,124)( 49,113)( 50,114)( 51,119)( 52,120)( 53,118)( 54,117)( 55,115)( 56,116)( 57,105)( 58,106)( 59,111)( 60,112)( 61,110)( 62,109)( 63,107)( 64,108)( 65, 97)( 66, 98)( 67,103)( 68,104)( 69,102)( 70,101)( 71, 99)( 72,100)(147,151)(148,152)(149,150)(153,161)(154,162)(155,167)(156,168)(157,166)(158,165)(159,163)(160,164)(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)(217,290)(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)(241,354)(242,353)(243,360)(244,359)(245,357)(246,358)(247,356)(248,355)(249,346)(250,345)(251,352)(252,351)(253,349)(254,350)(255,348)(256,347)(257,338)(258,337)(259,344)(260,343)(261,341)(262,342)(263,340)(264,339)(265,330)(266,329)(267,336)(268,335)(269,333)(270,334)(271,332)(272,331)(273,322)(274,321)(275,328)(276,327)(277,325)(278,326)(279,324)(280,323)(281,314)(282,313)(283,320)(284,319)(285,317)(286,318)(287,316)(288,315)(361,362)(363,368)(364,367)(369,378)(370,377)(371,384)(372,383)(373,381)(374,382)(375,380)(376,379)(385,426)(386,425)(387,432)(388,431)(389,429)(390,430)(391,428)(392,427)(393,418)(394,417)(395,424)(396,423)(397,421)(398,422)(399,420)(400,419)(401,410)(402,409)(403,416)(404,415)(405,413)(406,414)(407,412)(408,411); s2 := Sym(432)!( 1,243)( 2,244)( 3,241)( 4,242)( 5,246)( 6,245)( 7,247)( 8,248)( 9,259)( 10,260)( 11,257)( 12,258)( 13,262)( 14,261)( 15,263)( 16,264)( 17,251)( 18,252)( 19,249)( 20,250)( 21,254)( 22,253)( 23,255)( 24,256)( 25,219)( 26,220)( 27,217)( 28,218)( 29,222)( 30,221)( 31,223)( 32,224)( 33,235)( 34,236)( 35,233)( 36,234)( 37,238)( 38,237)( 39,239)( 40,240)( 41,227)( 42,228)( 43,225)( 44,226)( 45,230)( 46,229)( 47,231)( 48,232)( 49,283)( 50,284)( 51,281)( 52,282)( 53,286)( 54,285)( 55,287)( 56,288)( 57,275)( 58,276)( 59,273)( 60,274)( 61,278)( 62,277)( 63,279)( 64,280)( 65,267)( 66,268)( 67,265)( 68,266)( 69,270)( 70,269)( 71,271)( 72,272)( 73,387)( 74,388)( 75,385)( 76,386)( 77,390)( 78,389)( 79,391)( 80,392)( 81,403)( 82,404)( 83,401)( 84,402)( 85,406)( 86,405)( 87,407)( 88,408)( 89,395)( 90,396)( 91,393)( 92,394)( 93,398)( 94,397)( 95,399)( 96,400)( 97,363)( 98,364)( 99,361)(100,362)(101,366)(102,365)(103,367)(104,368)(105,379)(106,380)(107,377)(108,378)(109,382)(110,381)(111,383)(112,384)(113,371)(114,372)(115,369)(116,370)(117,374)(118,373)(119,375)(120,376)(121,427)(122,428)(123,425)(124,426)(125,430)(126,429)(127,431)(128,432)(129,419)(130,420)(131,417)(132,418)(133,422)(134,421)(135,423)(136,424)(137,411)(138,412)(139,409)(140,410)(141,414)(142,413)(143,415)(144,416)(145,315)(146,316)(147,313)(148,314)(149,318)(150,317)(151,319)(152,320)(153,331)(154,332)(155,329)(156,330)(157,334)(158,333)(159,335)(160,336)(161,323)(162,324)(163,321)(164,322)(165,326)(166,325)(167,327)(168,328)(169,291)(170,292)(171,289)(172,290)(173,294)(174,293)(175,295)(176,296)(177,307)(178,308)(179,305)(180,306)(181,310)(182,309)(183,311)(184,312)(185,299)(186,300)(187,297)(188,298)(189,302)(190,301)(191,303)(192,304)(193,355)(194,356)(195,353)(196,354)(197,358)(198,357)(199,359)(200,360)(201,347)(202,348)(203,345)(204,346)(205,350)(206,349)(207,351)(208,352)(209,339)(210,340)(211,337)(212,338)(213,342)(214,341)(215,343)(216,344); 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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s2*s1*s2*s0*s1*s0*s1*s2*s1*s2*s1*s2*s0*s1, s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s2*s1*s0, s2*s1*s0*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*s0*s2*s1*s2*s1 >;
References
None.
to this polytope.