Overview
- Group
- SmallGroup(1728,30298)
- Rank
- 4
- Schläfli Type
- {8,6,6}
- Vertices, edges, …
- 16, 72, 54, 9
- Order of s0s1s2s3
- 12
- Order of s0s1s2s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Universal
- Non-Orientable
- Flat
Quotients maximal quotients in bold
2-fold
4-fold
8-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 := ( 1,221)( 2,222)( 3,224)( 4,223)( 5,218)( 6,217)( 7,219)( 8,220)( 9,229)( 10,230)( 11,232)( 12,231)( 13,226)( 14,225)( 15,227)( 16,228)( 17,237)( 18,238)( 19,240)( 20,239)( 21,234)( 22,233)( 23,235)( 24,236)( 25,245)( 26,246)( 27,248)( 28,247)( 29,242)( 30,241)( 31,243)( 32,244)( 33,253)( 34,254)( 35,256)( 36,255)( 37,250)( 38,249)( 39,251)( 40,252)( 41,261)( 42,262)( 43,264)( 44,263)( 45,258)( 46,257)( 47,259)( 48,260)( 49,269)( 50,270)( 51,272)( 52,271)( 53,266)( 54,265)( 55,267)( 56,268)( 57,277)( 58,278)( 59,280)( 60,279)( 61,274)( 62,273)( 63,275)( 64,276)( 65,285)( 66,286)( 67,288)( 68,287)( 69,282)( 70,281)( 71,283)( 72,284)( 73,293)( 74,294)( 75,296)( 76,295)( 77,290)( 78,289)( 79,291)( 80,292)( 81,301)( 82,302)( 83,304)( 84,303)( 85,298)( 86,297)( 87,299)( 88,300)( 89,309)( 90,310)( 91,312)( 92,311)( 93,306)( 94,305)( 95,307)( 96,308)( 97,317)( 98,318)( 99,320)(100,319)(101,314)(102,313)(103,315)(104,316)(105,325)(106,326)(107,328)(108,327)(109,322)(110,321)(111,323)(112,324)(113,333)(114,334)(115,336)(116,335)(117,330)(118,329)(119,331)(120,332)(121,341)(122,342)(123,344)(124,343)(125,338)(126,337)(127,339)(128,340)(129,349)(130,350)(131,352)(132,351)(133,346)(134,345)(135,347)(136,348)(137,357)(138,358)(139,360)(140,359)(141,354)(142,353)(143,355)(144,356)(145,365)(146,366)(147,368)(148,367)(149,362)(150,361)(151,363)(152,364)(153,373)(154,374)(155,376)(156,375)(157,370)(158,369)(159,371)(160,372)(161,381)(162,382)(163,384)(164,383)(165,378)(166,377)(167,379)(168,380)(169,389)(170,390)(171,392)(172,391)(173,386)(174,385)(175,387)(176,388)(177,397)(178,398)(179,400)(180,399)(181,394)(182,393)(183,395)(184,396)(185,405)(186,406)(187,408)(188,407)(189,402)(190,401)(191,403)(192,404)(193,413)(194,414)(195,416)(196,415)(197,410)(198,409)(199,411)(200,412)(201,421)(202,422)(203,424)(204,423)(205,418)(206,417)(207,419)(208,420)(209,429)(210,430)(211,432)(212,431)(213,426)(214,425)(215,427)(216,428);; s1 := ( 3, 4)( 5, 7)( 6, 8)( 9, 17)( 10, 18)( 11, 20)( 12, 19)( 13, 23)( 14, 24)( 15, 21)( 16, 22)( 27, 28)( 29, 31)( 30, 32)( 33, 41)( 34, 42)( 35, 44)( 36, 43)( 37, 47)( 38, 48)( 39, 45)( 40, 46)( 51, 52)( 53, 55)( 54, 56)( 57, 65)( 58, 66)( 59, 68)( 60, 67)( 61, 71)( 62, 72)( 63, 69)( 64, 70)( 73,145)( 74,146)( 75,148)( 76,147)( 77,151)( 78,152)( 79,149)( 80,150)( 81,161)( 82,162)( 83,164)( 84,163)( 85,167)( 86,168)( 87,165)( 88,166)( 89,153)( 90,154)( 91,156)( 92,155)( 93,159)( 94,160)( 95,157)( 96,158)( 97,169)( 98,170)( 99,172)(100,171)(101,175)(102,176)(103,173)(104,174)(105,185)(106,186)(107,188)(108,187)(109,191)(110,192)(111,189)(112,190)(113,177)(114,178)(115,180)(116,179)(117,183)(118,184)(119,181)(120,182)(121,193)(122,194)(123,196)(124,195)(125,199)(126,200)(127,197)(128,198)(129,209)(130,210)(131,212)(132,211)(133,215)(134,216)(135,213)(136,214)(137,201)(138,202)(139,204)(140,203)(141,207)(142,208)(143,205)(144,206)(217,218)(221,224)(222,223)(225,234)(226,233)(227,235)(228,236)(229,240)(230,239)(231,238)(232,237)(241,242)(245,248)(246,247)(249,258)(250,257)(251,259)(252,260)(253,264)(254,263)(255,262)(256,261)(265,266)(269,272)(270,271)(273,282)(274,281)(275,283)(276,284)(277,288)(278,287)(279,286)(280,285)(289,362)(290,361)(291,363)(292,364)(293,368)(294,367)(295,366)(296,365)(297,378)(298,377)(299,379)(300,380)(301,384)(302,383)(303,382)(304,381)(305,370)(306,369)(307,371)(308,372)(309,376)(310,375)(311,374)(312,373)(313,386)(314,385)(315,387)(316,388)(317,392)(318,391)(319,390)(320,389)(321,402)(322,401)(323,403)(324,404)(325,408)(326,407)(327,406)(328,405)(329,394)(330,393)(331,395)(332,396)(333,400)(334,399)(335,398)(336,397)(337,410)(338,409)(339,411)(340,412)(341,416)(342,415)(343,414)(344,413)(345,426)(346,425)(347,427)(348,428)(349,432)(350,431)(351,430)(352,429)(353,418)(354,417)(355,419)(356,420)(357,424)(358,423)(359,422)(360,421);; s2 := ( 1, 73)( 2, 74)( 3, 79)( 4, 80)( 5, 78)( 6, 77)( 7, 75)( 8, 76)( 9, 81)( 10, 82)( 11, 87)( 12, 88)( 13, 86)( 14, 85)( 15, 83)( 16, 84)( 17, 89)( 18, 90)( 19, 95)( 20, 96)( 21, 94)( 22, 93)( 23, 91)( 24, 92)( 25,137)( 26,138)( 27,143)( 28,144)( 29,142)( 30,141)( 31,139)( 32,140)( 33,121)( 34,122)( 35,127)( 36,128)( 37,126)( 38,125)( 39,123)( 40,124)( 41,129)( 42,130)( 43,135)( 44,136)( 45,134)( 46,133)( 47,131)( 48,132)( 49,105)( 50,106)( 51,111)( 52,112)( 53,110)( 54,109)( 55,107)( 56,108)( 57,113)( 58,114)( 59,119)( 60,120)( 61,118)( 62,117)( 63,115)( 64,116)( 65, 97)( 66, 98)( 67,103)( 68,104)( 69,102)( 70,101)( 71, 99)( 72,100)(147,151)(148,152)(149,150)(155,159)(156,160)(157,158)(163,167)(164,168)(165,166)(169,209)(170,210)(171,215)(172,216)(173,214)(174,213)(175,211)(176,212)(177,193)(178,194)(179,199)(180,200)(181,198)(182,197)(183,195)(184,196)(185,201)(186,202)(187,207)(188,208)(189,206)(190,205)(191,203)(192,204)(217,290)(218,289)(219,296)(220,295)(221,293)(222,294)(223,292)(224,291)(225,298)(226,297)(227,304)(228,303)(229,301)(230,302)(231,300)(232,299)(233,306)(234,305)(235,312)(236,311)(237,309)(238,310)(239,308)(240,307)(241,354)(242,353)(243,360)(244,359)(245,357)(246,358)(247,356)(248,355)(249,338)(250,337)(251,344)(252,343)(253,341)(254,342)(255,340)(256,339)(257,346)(258,345)(259,352)(260,351)(261,349)(262,350)(263,348)(264,347)(265,322)(266,321)(267,328)(268,327)(269,325)(270,326)(271,324)(272,323)(273,330)(274,329)(275,336)(276,335)(277,333)(278,334)(279,332)(280,331)(281,314)(282,313)(283,320)(284,319)(285,317)(286,318)(287,316)(288,315)(361,362)(363,368)(364,367)(369,370)(371,376)(372,375)(377,378)(379,384)(380,383)(385,426)(386,425)(387,432)(388,431)(389,429)(390,430)(391,428)(392,427)(393,410)(394,409)(395,416)(396,415)(397,413)(398,414)(399,412)(400,411)(401,418)(402,417)(403,424)(404,423)(405,421)(406,422)(407,420)(408,419);; s3 := ( 1, 25)( 2, 26)( 3, 27)( 4, 28)( 5, 29)( 6, 30)( 7, 31)( 8, 32)( 9, 41)( 10, 42)( 11, 43)( 12, 44)( 13, 45)( 14, 46)( 15, 47)( 16, 48)( 17, 33)( 18, 34)( 19, 35)( 20, 36)( 21, 37)( 22, 38)( 23, 39)( 24, 40)( 57, 65)( 58, 66)( 59, 67)( 60, 68)( 61, 69)( 62, 70)( 63, 71)( 64, 72)( 73, 97)( 74, 98)( 75, 99)( 76,100)( 77,101)( 78,102)( 79,103)( 80,104)( 81,113)( 82,114)( 83,115)( 84,116)( 85,117)( 86,118)( 87,119)( 88,120)( 89,105)( 90,106)( 91,107)( 92,108)( 93,109)( 94,110)( 95,111)( 96,112)(129,137)(130,138)(131,139)(132,140)(133,141)(134,142)(135,143)(136,144)(145,169)(146,170)(147,171)(148,172)(149,173)(150,174)(151,175)(152,176)(153,185)(154,186)(155,187)(156,188)(157,189)(158,190)(159,191)(160,192)(161,177)(162,178)(163,179)(164,180)(165,181)(166,182)(167,183)(168,184)(201,209)(202,210)(203,211)(204,212)(205,213)(206,214)(207,215)(208,216)(217,241)(218,242)(219,243)(220,244)(221,245)(222,246)(223,247)(224,248)(225,257)(226,258)(227,259)(228,260)(229,261)(230,262)(231,263)(232,264)(233,249)(234,250)(235,251)(236,252)(237,253)(238,254)(239,255)(240,256)(273,281)(274,282)(275,283)(276,284)(277,285)(278,286)(279,287)(280,288)(289,313)(290,314)(291,315)(292,316)(293,317)(294,318)(295,319)(296,320)(297,329)(298,330)(299,331)(300,332)(301,333)(302,334)(303,335)(304,336)(305,321)(306,322)(307,323)(308,324)(309,325)(310,326)(311,327)(312,328)(345,353)(346,354)(347,355)(348,356)(349,357)(350,358)(351,359)(352,360)(361,385)(362,386)(363,387)(364,388)(365,389)(366,390)(367,391)(368,392)(369,401)(370,402)(371,403)(372,404)(373,405)(374,406)(375,407)(376,408)(377,393)(378,394)(379,395)(380,396)(381,397)(382,398)(383,399)(384,400)(417,425)(418,426)(419,427)(420,428)(421,429)(422,430)(423,431)(424,432);; 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*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s1*s2*s3*s1*s2*s3*s1*s2*s3,
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*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)( 9,229)( 10,230)( 11,232)( 12,231)( 13,226)( 14,225)( 15,227)( 16,228)( 17,237)( 18,238)( 19,240)( 20,239)( 21,234)( 22,233)( 23,235)( 24,236)( 25,245)( 26,246)( 27,248)( 28,247)( 29,242)( 30,241)( 31,243)( 32,244)( 33,253)( 34,254)( 35,256)( 36,255)( 37,250)( 38,249)( 39,251)( 40,252)( 41,261)( 42,262)( 43,264)( 44,263)( 45,258)( 46,257)( 47,259)( 48,260)( 49,269)( 50,270)( 51,272)( 52,271)( 53,266)( 54,265)( 55,267)( 56,268)( 57,277)( 58,278)( 59,280)( 60,279)( 61,274)( 62,273)( 63,275)( 64,276)( 65,285)( 66,286)( 67,288)( 68,287)( 69,282)( 70,281)( 71,283)( 72,284)( 73,293)( 74,294)( 75,296)( 76,295)( 77,290)( 78,289)( 79,291)( 80,292)( 81,301)( 82,302)( 83,304)( 84,303)( 85,298)( 86,297)( 87,299)( 88,300)( 89,309)( 90,310)( 91,312)( 92,311)( 93,306)( 94,305)( 95,307)( 96,308)( 97,317)( 98,318)( 99,320)(100,319)(101,314)(102,313)(103,315)(104,316)(105,325)(106,326)(107,328)(108,327)(109,322)(110,321)(111,323)(112,324)(113,333)(114,334)(115,336)(116,335)(117,330)(118,329)(119,331)(120,332)(121,341)(122,342)(123,344)(124,343)(125,338)(126,337)(127,339)(128,340)(129,349)(130,350)(131,352)(132,351)(133,346)(134,345)(135,347)(136,348)(137,357)(138,358)(139,360)(140,359)(141,354)(142,353)(143,355)(144,356)(145,365)(146,366)(147,368)(148,367)(149,362)(150,361)(151,363)(152,364)(153,373)(154,374)(155,376)(156,375)(157,370)(158,369)(159,371)(160,372)(161,381)(162,382)(163,384)(164,383)(165,378)(166,377)(167,379)(168,380)(169,389)(170,390)(171,392)(172,391)(173,386)(174,385)(175,387)(176,388)(177,397)(178,398)(179,400)(180,399)(181,394)(182,393)(183,395)(184,396)(185,405)(186,406)(187,408)(188,407)(189,402)(190,401)(191,403)(192,404)(193,413)(194,414)(195,416)(196,415)(197,410)(198,409)(199,411)(200,412)(201,421)(202,422)(203,424)(204,423)(205,418)(206,417)(207,419)(208,420)(209,429)(210,430)(211,432)(212,431)(213,426)(214,425)(215,427)(216,428); s1 := Sym(432)!( 3, 4)( 5, 7)( 6, 8)( 9, 17)( 10, 18)( 11, 20)( 12, 19)( 13, 23)( 14, 24)( 15, 21)( 16, 22)( 27, 28)( 29, 31)( 30, 32)( 33, 41)( 34, 42)( 35, 44)( 36, 43)( 37, 47)( 38, 48)( 39, 45)( 40, 46)( 51, 52)( 53, 55)( 54, 56)( 57, 65)( 58, 66)( 59, 68)( 60, 67)( 61, 71)( 62, 72)( 63, 69)( 64, 70)( 73,145)( 74,146)( 75,148)( 76,147)( 77,151)( 78,152)( 79,149)( 80,150)( 81,161)( 82,162)( 83,164)( 84,163)( 85,167)( 86,168)( 87,165)( 88,166)( 89,153)( 90,154)( 91,156)( 92,155)( 93,159)( 94,160)( 95,157)( 96,158)( 97,169)( 98,170)( 99,172)(100,171)(101,175)(102,176)(103,173)(104,174)(105,185)(106,186)(107,188)(108,187)(109,191)(110,192)(111,189)(112,190)(113,177)(114,178)(115,180)(116,179)(117,183)(118,184)(119,181)(120,182)(121,193)(122,194)(123,196)(124,195)(125,199)(126,200)(127,197)(128,198)(129,209)(130,210)(131,212)(132,211)(133,215)(134,216)(135,213)(136,214)(137,201)(138,202)(139,204)(140,203)(141,207)(142,208)(143,205)(144,206)(217,218)(221,224)(222,223)(225,234)(226,233)(227,235)(228,236)(229,240)(230,239)(231,238)(232,237)(241,242)(245,248)(246,247)(249,258)(250,257)(251,259)(252,260)(253,264)(254,263)(255,262)(256,261)(265,266)(269,272)(270,271)(273,282)(274,281)(275,283)(276,284)(277,288)(278,287)(279,286)(280,285)(289,362)(290,361)(291,363)(292,364)(293,368)(294,367)(295,366)(296,365)(297,378)(298,377)(299,379)(300,380)(301,384)(302,383)(303,382)(304,381)(305,370)(306,369)(307,371)(308,372)(309,376)(310,375)(311,374)(312,373)(313,386)(314,385)(315,387)(316,388)(317,392)(318,391)(319,390)(320,389)(321,402)(322,401)(323,403)(324,404)(325,408)(326,407)(327,406)(328,405)(329,394)(330,393)(331,395)(332,396)(333,400)(334,399)(335,398)(336,397)(337,410)(338,409)(339,411)(340,412)(341,416)(342,415)(343,414)(344,413)(345,426)(346,425)(347,427)(348,428)(349,432)(350,431)(351,430)(352,429)(353,418)(354,417)(355,419)(356,420)(357,424)(358,423)(359,422)(360,421); s2 := Sym(432)!( 1, 73)( 2, 74)( 3, 79)( 4, 80)( 5, 78)( 6, 77)( 7, 75)( 8, 76)( 9, 81)( 10, 82)( 11, 87)( 12, 88)( 13, 86)( 14, 85)( 15, 83)( 16, 84)( 17, 89)( 18, 90)( 19, 95)( 20, 96)( 21, 94)( 22, 93)( 23, 91)( 24, 92)( 25,137)( 26,138)( 27,143)( 28,144)( 29,142)( 30,141)( 31,139)( 32,140)( 33,121)( 34,122)( 35,127)( 36,128)( 37,126)( 38,125)( 39,123)( 40,124)( 41,129)( 42,130)( 43,135)( 44,136)( 45,134)( 46,133)( 47,131)( 48,132)( 49,105)( 50,106)( 51,111)( 52,112)( 53,110)( 54,109)( 55,107)( 56,108)( 57,113)( 58,114)( 59,119)( 60,120)( 61,118)( 62,117)( 63,115)( 64,116)( 65, 97)( 66, 98)( 67,103)( 68,104)( 69,102)( 70,101)( 71, 99)( 72,100)(147,151)(148,152)(149,150)(155,159)(156,160)(157,158)(163,167)(164,168)(165,166)(169,209)(170,210)(171,215)(172,216)(173,214)(174,213)(175,211)(176,212)(177,193)(178,194)(179,199)(180,200)(181,198)(182,197)(183,195)(184,196)(185,201)(186,202)(187,207)(188,208)(189,206)(190,205)(191,203)(192,204)(217,290)(218,289)(219,296)(220,295)(221,293)(222,294)(223,292)(224,291)(225,298)(226,297)(227,304)(228,303)(229,301)(230,302)(231,300)(232,299)(233,306)(234,305)(235,312)(236,311)(237,309)(238,310)(239,308)(240,307)(241,354)(242,353)(243,360)(244,359)(245,357)(246,358)(247,356)(248,355)(249,338)(250,337)(251,344)(252,343)(253,341)(254,342)(255,340)(256,339)(257,346)(258,345)(259,352)(260,351)(261,349)(262,350)(263,348)(264,347)(265,322)(266,321)(267,328)(268,327)(269,325)(270,326)(271,324)(272,323)(273,330)(274,329)(275,336)(276,335)(277,333)(278,334)(279,332)(280,331)(281,314)(282,313)(283,320)(284,319)(285,317)(286,318)(287,316)(288,315)(361,362)(363,368)(364,367)(369,370)(371,376)(372,375)(377,378)(379,384)(380,383)(385,426)(386,425)(387,432)(388,431)(389,429)(390,430)(391,428)(392,427)(393,410)(394,409)(395,416)(396,415)(397,413)(398,414)(399,412)(400,411)(401,418)(402,417)(403,424)(404,423)(405,421)(406,422)(407,420)(408,419); s3 := Sym(432)!( 1, 25)( 2, 26)( 3, 27)( 4, 28)( 5, 29)( 6, 30)( 7, 31)( 8, 32)( 9, 41)( 10, 42)( 11, 43)( 12, 44)( 13, 45)( 14, 46)( 15, 47)( 16, 48)( 17, 33)( 18, 34)( 19, 35)( 20, 36)( 21, 37)( 22, 38)( 23, 39)( 24, 40)( 57, 65)( 58, 66)( 59, 67)( 60, 68)( 61, 69)( 62, 70)( 63, 71)( 64, 72)( 73, 97)( 74, 98)( 75, 99)( 76,100)( 77,101)( 78,102)( 79,103)( 80,104)( 81,113)( 82,114)( 83,115)( 84,116)( 85,117)( 86,118)( 87,119)( 88,120)( 89,105)( 90,106)( 91,107)( 92,108)( 93,109)( 94,110)( 95,111)( 96,112)(129,137)(130,138)(131,139)(132,140)(133,141)(134,142)(135,143)(136,144)(145,169)(146,170)(147,171)(148,172)(149,173)(150,174)(151,175)(152,176)(153,185)(154,186)(155,187)(156,188)(157,189)(158,190)(159,191)(160,192)(161,177)(162,178)(163,179)(164,180)(165,181)(166,182)(167,183)(168,184)(201,209)(202,210)(203,211)(204,212)(205,213)(206,214)(207,215)(208,216)(217,241)(218,242)(219,243)(220,244)(221,245)(222,246)(223,247)(224,248)(225,257)(226,258)(227,259)(228,260)(229,261)(230,262)(231,263)(232,264)(233,249)(234,250)(235,251)(236,252)(237,253)(238,254)(239,255)(240,256)(273,281)(274,282)(275,283)(276,284)(277,285)(278,286)(279,287)(280,288)(289,313)(290,314)(291,315)(292,316)(293,317)(294,318)(295,319)(296,320)(297,329)(298,330)(299,331)(300,332)(301,333)(302,334)(303,335)(304,336)(305,321)(306,322)(307,323)(308,324)(309,325)(310,326)(311,327)(312,328)(345,353)(346,354)(347,355)(348,356)(349,357)(350,358)(351,359)(352,360)(361,385)(362,386)(363,387)(364,388)(365,389)(366,390)(367,391)(368,392)(369,401)(370,402)(371,403)(372,404)(373,405)(374,406)(375,407)(376,408)(377,393)(378,394)(379,395)(380,396)(381,397)(382,398)(383,399)(384,400)(417,425)(418,426)(419,427)(420,428)(421,429)(422,430)(423,431)(424,432); poly := sub<Sym(432)|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*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, s1*s2*s3*s1*s2*s3*s1*s2*s3, s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1 >;
References
None.
to this polytope.