Overview
- Group
- SmallGroup(1728,30374)
- Rank
- 4
- Schläfli Type
- {2,6,24}
- Vertices, edges, …
- 2, 18, 216, 72
- Order of s0s1s2s3
- 24
- Order of s0s1s2s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Degenerate
- Universal
- Orientable
- Flat
Quotients maximal quotients in bold
2-fold
3-fold
4-fold
6-fold
12-fold
27-fold
54-fold
108-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := ( 3,165)( 4,166)( 5,167)( 6,173)( 7,171)( 8,172)( 9,169)( 10,170)( 11,168)( 12,183)( 13,184)( 14,185)( 15,191)( 16,189)( 17,190)( 18,187)( 19,188)( 20,186)( 21,174)( 22,175)( 23,176)( 24,182)( 25,180)( 26,181)( 27,178)( 28,179)( 29,177)( 30,192)( 31,193)( 32,194)( 33,200)( 34,198)( 35,199)( 36,196)( 37,197)( 38,195)( 39,210)( 40,211)( 41,212)( 42,218)( 43,216)( 44,217)( 45,214)( 46,215)( 47,213)( 48,201)( 49,202)( 50,203)( 51,209)( 52,207)( 53,208)( 54,205)( 55,206)( 56,204)( 57,138)( 58,139)( 59,140)( 60,146)( 61,144)( 62,145)( 63,142)( 64,143)( 65,141)( 66,156)( 67,157)( 68,158)( 69,164)( 70,162)( 71,163)( 72,160)( 73,161)( 74,159)( 75,147)( 76,148)( 77,149)( 78,155)( 79,153)( 80,154)( 81,151)( 82,152)( 83,150)( 84,111)( 85,112)( 86,113)( 87,119)( 88,117)( 89,118)( 90,115)( 91,116)( 92,114)( 93,129)( 94,130)( 95,131)( 96,137)( 97,135)( 98,136)( 99,133)(100,134)(101,132)(102,120)(103,121)(104,122)(105,128)(106,126)(107,127)(108,124)(109,125)(110,123)(219,381)(220,382)(221,383)(222,389)(223,387)(224,388)(225,385)(226,386)(227,384)(228,399)(229,400)(230,401)(231,407)(232,405)(233,406)(234,403)(235,404)(236,402)(237,390)(238,391)(239,392)(240,398)(241,396)(242,397)(243,394)(244,395)(245,393)(246,408)(247,409)(248,410)(249,416)(250,414)(251,415)(252,412)(253,413)(254,411)(255,426)(256,427)(257,428)(258,434)(259,432)(260,433)(261,430)(262,431)(263,429)(264,417)(265,418)(266,419)(267,425)(268,423)(269,424)(270,421)(271,422)(272,420)(273,354)(274,355)(275,356)(276,362)(277,360)(278,361)(279,358)(280,359)(281,357)(282,372)(283,373)(284,374)(285,380)(286,378)(287,379)(288,376)(289,377)(290,375)(291,363)(292,364)(293,365)(294,371)(295,369)(296,370)(297,367)(298,368)(299,366)(300,327)(301,328)(302,329)(303,335)(304,333)(305,334)(306,331)(307,332)(308,330)(309,345)(310,346)(311,347)(312,353)(313,351)(314,352)(315,349)(316,350)(317,348)(318,336)(319,337)(320,338)(321,344)(322,342)(323,343)(324,340)(325,341)(326,339);; s2 := ( 3, 12)( 4, 14)( 5, 13)( 6, 17)( 7, 16)( 8, 15)( 9, 19)( 10, 18)( 11, 20)( 22, 23)( 24, 26)( 27, 28)( 30, 39)( 31, 41)( 32, 40)( 33, 44)( 34, 43)( 35, 42)( 36, 46)( 37, 45)( 38, 47)( 49, 50)( 51, 53)( 54, 55)( 57, 93)( 58, 95)( 59, 94)( 60, 98)( 61, 97)( 62, 96)( 63,100)( 64, 99)( 65,101)( 66, 84)( 67, 86)( 68, 85)( 69, 89)( 70, 88)( 71, 87)( 72, 91)( 73, 90)( 74, 92)( 75,102)( 76,104)( 77,103)( 78,107)( 79,106)( 80,105)( 81,109)( 82,108)( 83,110)(111,147)(112,149)(113,148)(114,152)(115,151)(116,150)(117,154)(118,153)(119,155)(120,138)(121,140)(122,139)(123,143)(124,142)(125,141)(126,145)(127,144)(128,146)(129,156)(130,158)(131,157)(132,161)(133,160)(134,159)(135,163)(136,162)(137,164)(165,174)(166,176)(167,175)(168,179)(169,178)(170,177)(171,181)(172,180)(173,182)(184,185)(186,188)(189,190)(192,201)(193,203)(194,202)(195,206)(196,205)(197,204)(198,208)(199,207)(200,209)(211,212)(213,215)(216,217)(219,282)(220,284)(221,283)(222,287)(223,286)(224,285)(225,289)(226,288)(227,290)(228,273)(229,275)(230,274)(231,278)(232,277)(233,276)(234,280)(235,279)(236,281)(237,291)(238,293)(239,292)(240,296)(241,295)(242,294)(243,298)(244,297)(245,299)(246,309)(247,311)(248,310)(249,314)(250,313)(251,312)(252,316)(253,315)(254,317)(255,300)(256,302)(257,301)(258,305)(259,304)(260,303)(261,307)(262,306)(263,308)(264,318)(265,320)(266,319)(267,323)(268,322)(269,321)(270,325)(271,324)(272,326)(327,417)(328,419)(329,418)(330,422)(331,421)(332,420)(333,424)(334,423)(335,425)(336,408)(337,410)(338,409)(339,413)(340,412)(341,411)(342,415)(343,414)(344,416)(345,426)(346,428)(347,427)(348,431)(349,430)(350,429)(351,433)(352,432)(353,434)(354,390)(355,392)(356,391)(357,395)(358,394)(359,393)(360,397)(361,396)(362,398)(363,381)(364,383)(365,382)(366,386)(367,385)(368,384)(369,388)(370,387)(371,389)(372,399)(373,401)(374,400)(375,404)(376,403)(377,402)(378,406)(379,405)(380,407);; s3 := ( 3,219)( 4,221)( 5,220)( 6,230)( 7,229)( 8,228)( 9,238)( 10,237)( 11,239)( 12,224)( 13,223)( 14,222)( 15,233)( 16,232)( 17,231)( 18,242)( 19,241)( 20,240)( 21,226)( 22,225)( 23,227)( 24,236)( 25,235)( 26,234)( 27,243)( 28,245)( 29,244)( 30,246)( 31,248)( 32,247)( 33,257)( 34,256)( 35,255)( 36,265)( 37,264)( 38,266)( 39,251)( 40,250)( 41,249)( 42,260)( 43,259)( 44,258)( 45,269)( 46,268)( 47,267)( 48,253)( 49,252)( 50,254)( 51,263)( 52,262)( 53,261)( 54,270)( 55,272)( 56,271)( 57,300)( 58,302)( 59,301)( 60,311)( 61,310)( 62,309)( 63,319)( 64,318)( 65,320)( 66,305)( 67,304)( 68,303)( 69,314)( 70,313)( 71,312)( 72,323)( 73,322)( 74,321)( 75,307)( 76,306)( 77,308)( 78,317)( 79,316)( 80,315)( 81,324)( 82,326)( 83,325)( 84,273)( 85,275)( 86,274)( 87,284)( 88,283)( 89,282)( 90,292)( 91,291)( 92,293)( 93,278)( 94,277)( 95,276)( 96,287)( 97,286)( 98,285)( 99,296)(100,295)(101,294)(102,280)(103,279)(104,281)(105,290)(106,289)(107,288)(108,297)(109,299)(110,298)(111,354)(112,356)(113,355)(114,365)(115,364)(116,363)(117,373)(118,372)(119,374)(120,359)(121,358)(122,357)(123,368)(124,367)(125,366)(126,377)(127,376)(128,375)(129,361)(130,360)(131,362)(132,371)(133,370)(134,369)(135,378)(136,380)(137,379)(138,327)(139,329)(140,328)(141,338)(142,337)(143,336)(144,346)(145,345)(146,347)(147,332)(148,331)(149,330)(150,341)(151,340)(152,339)(153,350)(154,349)(155,348)(156,334)(157,333)(158,335)(159,344)(160,343)(161,342)(162,351)(163,353)(164,352)(165,381)(166,383)(167,382)(168,392)(169,391)(170,390)(171,400)(172,399)(173,401)(174,386)(175,385)(176,384)(177,395)(178,394)(179,393)(180,404)(181,403)(182,402)(183,388)(184,387)(185,389)(186,398)(187,397)(188,396)(189,405)(190,407)(191,406)(192,408)(193,410)(194,409)(195,419)(196,418)(197,417)(198,427)(199,426)(200,428)(201,413)(202,412)(203,411)(204,422)(205,421)(206,420)(207,431)(208,430)(209,429)(210,415)(211,414)(212,416)(213,425)(214,424)(215,423)(216,432)(217,434)(218,433);; poly := Group([s0,s1,s2,s3]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2*s3*s2,
s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s1,
s1*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2*s3*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(434)!(1,2); s1 := Sym(434)!( 3,165)( 4,166)( 5,167)( 6,173)( 7,171)( 8,172)( 9,169)( 10,170)( 11,168)( 12,183)( 13,184)( 14,185)( 15,191)( 16,189)( 17,190)( 18,187)( 19,188)( 20,186)( 21,174)( 22,175)( 23,176)( 24,182)( 25,180)( 26,181)( 27,178)( 28,179)( 29,177)( 30,192)( 31,193)( 32,194)( 33,200)( 34,198)( 35,199)( 36,196)( 37,197)( 38,195)( 39,210)( 40,211)( 41,212)( 42,218)( 43,216)( 44,217)( 45,214)( 46,215)( 47,213)( 48,201)( 49,202)( 50,203)( 51,209)( 52,207)( 53,208)( 54,205)( 55,206)( 56,204)( 57,138)( 58,139)( 59,140)( 60,146)( 61,144)( 62,145)( 63,142)( 64,143)( 65,141)( 66,156)( 67,157)( 68,158)( 69,164)( 70,162)( 71,163)( 72,160)( 73,161)( 74,159)( 75,147)( 76,148)( 77,149)( 78,155)( 79,153)( 80,154)( 81,151)( 82,152)( 83,150)( 84,111)( 85,112)( 86,113)( 87,119)( 88,117)( 89,118)( 90,115)( 91,116)( 92,114)( 93,129)( 94,130)( 95,131)( 96,137)( 97,135)( 98,136)( 99,133)(100,134)(101,132)(102,120)(103,121)(104,122)(105,128)(106,126)(107,127)(108,124)(109,125)(110,123)(219,381)(220,382)(221,383)(222,389)(223,387)(224,388)(225,385)(226,386)(227,384)(228,399)(229,400)(230,401)(231,407)(232,405)(233,406)(234,403)(235,404)(236,402)(237,390)(238,391)(239,392)(240,398)(241,396)(242,397)(243,394)(244,395)(245,393)(246,408)(247,409)(248,410)(249,416)(250,414)(251,415)(252,412)(253,413)(254,411)(255,426)(256,427)(257,428)(258,434)(259,432)(260,433)(261,430)(262,431)(263,429)(264,417)(265,418)(266,419)(267,425)(268,423)(269,424)(270,421)(271,422)(272,420)(273,354)(274,355)(275,356)(276,362)(277,360)(278,361)(279,358)(280,359)(281,357)(282,372)(283,373)(284,374)(285,380)(286,378)(287,379)(288,376)(289,377)(290,375)(291,363)(292,364)(293,365)(294,371)(295,369)(296,370)(297,367)(298,368)(299,366)(300,327)(301,328)(302,329)(303,335)(304,333)(305,334)(306,331)(307,332)(308,330)(309,345)(310,346)(311,347)(312,353)(313,351)(314,352)(315,349)(316,350)(317,348)(318,336)(319,337)(320,338)(321,344)(322,342)(323,343)(324,340)(325,341)(326,339); s2 := Sym(434)!( 3, 12)( 4, 14)( 5, 13)( 6, 17)( 7, 16)( 8, 15)( 9, 19)( 10, 18)( 11, 20)( 22, 23)( 24, 26)( 27, 28)( 30, 39)( 31, 41)( 32, 40)( 33, 44)( 34, 43)( 35, 42)( 36, 46)( 37, 45)( 38, 47)( 49, 50)( 51, 53)( 54, 55)( 57, 93)( 58, 95)( 59, 94)( 60, 98)( 61, 97)( 62, 96)( 63,100)( 64, 99)( 65,101)( 66, 84)( 67, 86)( 68, 85)( 69, 89)( 70, 88)( 71, 87)( 72, 91)( 73, 90)( 74, 92)( 75,102)( 76,104)( 77,103)( 78,107)( 79,106)( 80,105)( 81,109)( 82,108)( 83,110)(111,147)(112,149)(113,148)(114,152)(115,151)(116,150)(117,154)(118,153)(119,155)(120,138)(121,140)(122,139)(123,143)(124,142)(125,141)(126,145)(127,144)(128,146)(129,156)(130,158)(131,157)(132,161)(133,160)(134,159)(135,163)(136,162)(137,164)(165,174)(166,176)(167,175)(168,179)(169,178)(170,177)(171,181)(172,180)(173,182)(184,185)(186,188)(189,190)(192,201)(193,203)(194,202)(195,206)(196,205)(197,204)(198,208)(199,207)(200,209)(211,212)(213,215)(216,217)(219,282)(220,284)(221,283)(222,287)(223,286)(224,285)(225,289)(226,288)(227,290)(228,273)(229,275)(230,274)(231,278)(232,277)(233,276)(234,280)(235,279)(236,281)(237,291)(238,293)(239,292)(240,296)(241,295)(242,294)(243,298)(244,297)(245,299)(246,309)(247,311)(248,310)(249,314)(250,313)(251,312)(252,316)(253,315)(254,317)(255,300)(256,302)(257,301)(258,305)(259,304)(260,303)(261,307)(262,306)(263,308)(264,318)(265,320)(266,319)(267,323)(268,322)(269,321)(270,325)(271,324)(272,326)(327,417)(328,419)(329,418)(330,422)(331,421)(332,420)(333,424)(334,423)(335,425)(336,408)(337,410)(338,409)(339,413)(340,412)(341,411)(342,415)(343,414)(344,416)(345,426)(346,428)(347,427)(348,431)(349,430)(350,429)(351,433)(352,432)(353,434)(354,390)(355,392)(356,391)(357,395)(358,394)(359,393)(360,397)(361,396)(362,398)(363,381)(364,383)(365,382)(366,386)(367,385)(368,384)(369,388)(370,387)(371,389)(372,399)(373,401)(374,400)(375,404)(376,403)(377,402)(378,406)(379,405)(380,407); s3 := Sym(434)!( 3,219)( 4,221)( 5,220)( 6,230)( 7,229)( 8,228)( 9,238)( 10,237)( 11,239)( 12,224)( 13,223)( 14,222)( 15,233)( 16,232)( 17,231)( 18,242)( 19,241)( 20,240)( 21,226)( 22,225)( 23,227)( 24,236)( 25,235)( 26,234)( 27,243)( 28,245)( 29,244)( 30,246)( 31,248)( 32,247)( 33,257)( 34,256)( 35,255)( 36,265)( 37,264)( 38,266)( 39,251)( 40,250)( 41,249)( 42,260)( 43,259)( 44,258)( 45,269)( 46,268)( 47,267)( 48,253)( 49,252)( 50,254)( 51,263)( 52,262)( 53,261)( 54,270)( 55,272)( 56,271)( 57,300)( 58,302)( 59,301)( 60,311)( 61,310)( 62,309)( 63,319)( 64,318)( 65,320)( 66,305)( 67,304)( 68,303)( 69,314)( 70,313)( 71,312)( 72,323)( 73,322)( 74,321)( 75,307)( 76,306)( 77,308)( 78,317)( 79,316)( 80,315)( 81,324)( 82,326)( 83,325)( 84,273)( 85,275)( 86,274)( 87,284)( 88,283)( 89,282)( 90,292)( 91,291)( 92,293)( 93,278)( 94,277)( 95,276)( 96,287)( 97,286)( 98,285)( 99,296)(100,295)(101,294)(102,280)(103,279)(104,281)(105,290)(106,289)(107,288)(108,297)(109,299)(110,298)(111,354)(112,356)(113,355)(114,365)(115,364)(116,363)(117,373)(118,372)(119,374)(120,359)(121,358)(122,357)(123,368)(124,367)(125,366)(126,377)(127,376)(128,375)(129,361)(130,360)(131,362)(132,371)(133,370)(134,369)(135,378)(136,380)(137,379)(138,327)(139,329)(140,328)(141,338)(142,337)(143,336)(144,346)(145,345)(146,347)(147,332)(148,331)(149,330)(150,341)(151,340)(152,339)(153,350)(154,349)(155,348)(156,334)(157,333)(158,335)(159,344)(160,343)(161,342)(162,351)(163,353)(164,352)(165,381)(166,383)(167,382)(168,392)(169,391)(170,390)(171,400)(172,399)(173,401)(174,386)(175,385)(176,384)(177,395)(178,394)(179,393)(180,404)(181,403)(182,402)(183,388)(184,387)(185,389)(186,398)(187,397)(188,396)(189,405)(190,407)(191,406)(192,408)(193,410)(194,409)(195,419)(196,418)(197,417)(198,427)(199,426)(200,428)(201,413)(202,412)(203,411)(204,422)(205,421)(206,420)(207,431)(208,430)(209,429)(210,415)(211,414)(212,416)(213,425)(214,424)(215,423)(216,432)(217,434)(218,433); poly := sub<Sym(434)|s0,s1,s2,s3>;
Finitely Presented Group Representation (Magma)
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2*s3*s2, s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s1, s1*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2*s3*s2 >;