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