Overview
- Group
- SmallGroup(1728,30189)
- Rank
- 3
- Schläfli Type
- {6,72}
- Vertices, edges, …
- 12, 432, 144
- 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
3-fold
4-fold
6-fold
8-fold
9-fold
12-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)(217,289)(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)(241,353)(242,354)(243,359)(244,360)(245,358)(246,357)(247,355)(248,356)(249,345)(250,346)(251,351)(252,352)(253,350)(254,349)(255,347)(256,348)(257,337)(258,338)(259,343)(260,344)(261,342)(262,341)(263,339)(264,340)(265,329)(266,330)(267,335)(268,336)(269,334)(270,333)(271,331)(272,332)(273,321)(274,322)(275,327)(276,328)(277,326)(278,325)(279,323)(280,324)(281,313)(282,314)(283,319)(284,320)(285,318)(286,317)(287,315)(288,316)(363,367)(364,368)(365,366)(369,377)(370,378)(371,383)(372,384)(373,382)(374,381)(375,379)(376,380)(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)( 9,259)( 10,260)( 11,258)( 12,257)( 13,263)( 14,264)( 15,262)( 16,261)( 17,251)( 18,252)( 19,250)( 20,249)( 21,255)( 22,256)( 23,254)( 24,253)( 25,219)( 26,220)( 27,218)( 28,217)( 29,223)( 30,224)( 31,222)( 32,221)( 33,235)( 34,236)( 35,234)( 36,233)( 37,239)( 38,240)( 39,238)( 40,237)( 41,227)( 42,228)( 43,226)( 44,225)( 45,231)( 46,232)( 47,230)( 48,229)( 49,283)( 50,284)( 51,282)( 52,281)( 53,287)( 54,288)( 55,286)( 56,285)( 57,275)( 58,276)( 59,274)( 60,273)( 61,279)( 62,280)( 63,278)( 64,277)( 65,267)( 66,268)( 67,266)( 68,265)( 69,271)( 70,272)( 71,270)( 72,269)( 73,315)( 74,316)( 75,314)( 76,313)( 77,319)( 78,320)( 79,318)( 80,317)( 81,331)( 82,332)( 83,330)( 84,329)( 85,335)( 86,336)( 87,334)( 88,333)( 89,323)( 90,324)( 91,322)( 92,321)( 93,327)( 94,328)( 95,326)( 96,325)( 97,291)( 98,292)( 99,290)(100,289)(101,295)(102,296)(103,294)(104,293)(105,307)(106,308)(107,306)(108,305)(109,311)(110,312)(111,310)(112,309)(113,299)(114,300)(115,298)(116,297)(117,303)(118,304)(119,302)(120,301)(121,355)(122,356)(123,354)(124,353)(125,359)(126,360)(127,358)(128,357)(129,347)(130,348)(131,346)(132,345)(133,351)(134,352)(135,350)(136,349)(137,339)(138,340)(139,338)(140,337)(141,343)(142,344)(143,342)(144,341)(145,387)(146,388)(147,386)(148,385)(149,391)(150,392)(151,390)(152,389)(153,403)(154,404)(155,402)(156,401)(157,407)(158,408)(159,406)(160,405)(161,395)(162,396)(163,394)(164,393)(165,399)(166,400)(167,398)(168,397)(169,363)(170,364)(171,362)(172,361)(173,367)(174,368)(175,366)(176,365)(177,379)(178,380)(179,378)(180,377)(181,383)(182,384)(183,382)(184,381)(185,371)(186,372)(187,370)(188,369)(189,375)(190,376)(191,374)(192,373)(193,427)(194,428)(195,426)(196,425)(197,431)(198,432)(199,430)(200,429)(201,419)(202,420)(203,418)(204,417)(205,423)(206,424)(207,422)(208,421)(209,411)(210,412)(211,410)(212,409)(213,415)(214,416)(215,414)(216,413);; 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*s1*s0*s1*s2*s1*s2*s1*s2*s1,
s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2 ];;
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)(217,289)(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)(241,353)(242,354)(243,359)(244,360)(245,358)(246,357)(247,355)(248,356)(249,345)(250,346)(251,351)(252,352)(253,350)(254,349)(255,347)(256,348)(257,337)(258,338)(259,343)(260,344)(261,342)(262,341)(263,339)(264,340)(265,329)(266,330)(267,335)(268,336)(269,334)(270,333)(271,331)(272,332)(273,321)(274,322)(275,327)(276,328)(277,326)(278,325)(279,323)(280,324)(281,313)(282,314)(283,319)(284,320)(285,318)(286,317)(287,315)(288,316)(363,367)(364,368)(365,366)(369,377)(370,378)(371,383)(372,384)(373,382)(374,381)(375,379)(376,380)(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)( 9,259)( 10,260)( 11,258)( 12,257)( 13,263)( 14,264)( 15,262)( 16,261)( 17,251)( 18,252)( 19,250)( 20,249)( 21,255)( 22,256)( 23,254)( 24,253)( 25,219)( 26,220)( 27,218)( 28,217)( 29,223)( 30,224)( 31,222)( 32,221)( 33,235)( 34,236)( 35,234)( 36,233)( 37,239)( 38,240)( 39,238)( 40,237)( 41,227)( 42,228)( 43,226)( 44,225)( 45,231)( 46,232)( 47,230)( 48,229)( 49,283)( 50,284)( 51,282)( 52,281)( 53,287)( 54,288)( 55,286)( 56,285)( 57,275)( 58,276)( 59,274)( 60,273)( 61,279)( 62,280)( 63,278)( 64,277)( 65,267)( 66,268)( 67,266)( 68,265)( 69,271)( 70,272)( 71,270)( 72,269)( 73,315)( 74,316)( 75,314)( 76,313)( 77,319)( 78,320)( 79,318)( 80,317)( 81,331)( 82,332)( 83,330)( 84,329)( 85,335)( 86,336)( 87,334)( 88,333)( 89,323)( 90,324)( 91,322)( 92,321)( 93,327)( 94,328)( 95,326)( 96,325)( 97,291)( 98,292)( 99,290)(100,289)(101,295)(102,296)(103,294)(104,293)(105,307)(106,308)(107,306)(108,305)(109,311)(110,312)(111,310)(112,309)(113,299)(114,300)(115,298)(116,297)(117,303)(118,304)(119,302)(120,301)(121,355)(122,356)(123,354)(124,353)(125,359)(126,360)(127,358)(128,357)(129,347)(130,348)(131,346)(132,345)(133,351)(134,352)(135,350)(136,349)(137,339)(138,340)(139,338)(140,337)(141,343)(142,344)(143,342)(144,341)(145,387)(146,388)(147,386)(148,385)(149,391)(150,392)(151,390)(152,389)(153,403)(154,404)(155,402)(156,401)(157,407)(158,408)(159,406)(160,405)(161,395)(162,396)(163,394)(164,393)(165,399)(166,400)(167,398)(168,397)(169,363)(170,364)(171,362)(172,361)(173,367)(174,368)(175,366)(176,365)(177,379)(178,380)(179,378)(180,377)(181,383)(182,384)(183,382)(184,381)(185,371)(186,372)(187,370)(188,369)(189,375)(190,376)(191,374)(192,373)(193,427)(194,428)(195,426)(196,425)(197,431)(198,432)(199,430)(200,429)(201,419)(202,420)(203,418)(204,417)(205,423)(206,424)(207,422)(208,421)(209,411)(210,412)(211,410)(212,409)(213,415)(214,416)(215,414)(216,413); 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*s1*s0*s1*s2*s1*s2*s1*s2*s1, s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2 >;
References
None.
to this polytope.