Overview
- Group
- SmallGroup(1728,36607)
- 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
9-fold
12-fold
18-fold
24-fold
27-fold
36-fold
54-fold
72-fold
108-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := ( 3,381)( 4,382)( 5,383)( 6,387)( 7,388)( 8,389)( 9,384)( 10,385)( 11,386)( 12,399)( 13,400)( 14,401)( 15,405)( 16,406)( 17,407)( 18,402)( 19,403)( 20,404)( 21,390)( 22,391)( 23,392)( 24,396)( 25,397)( 26,398)( 27,393)( 28,394)( 29,395)( 30,408)( 31,409)( 32,410)( 33,414)( 34,415)( 35,416)( 36,411)( 37,412)( 38,413)( 39,426)( 40,427)( 41,428)( 42,432)( 43,433)( 44,434)( 45,429)( 46,430)( 47,431)( 48,417)( 49,418)( 50,419)( 51,423)( 52,424)( 53,425)( 54,420)( 55,421)( 56,422)( 57,354)( 58,355)( 59,356)( 60,360)( 61,361)( 62,362)( 63,357)( 64,358)( 65,359)( 66,372)( 67,373)( 68,374)( 69,378)( 70,379)( 71,380)( 72,375)( 73,376)( 74,377)( 75,363)( 76,364)( 77,365)( 78,369)( 79,370)( 80,371)( 81,366)( 82,367)( 83,368)( 84,327)( 85,328)( 86,329)( 87,333)( 88,334)( 89,335)( 90,330)( 91,331)( 92,332)( 93,345)( 94,346)( 95,347)( 96,351)( 97,352)( 98,353)( 99,348)(100,349)(101,350)(102,336)(103,337)(104,338)(105,342)(106,343)(107,344)(108,339)(109,340)(110,341)(111,219)(112,220)(113,221)(114,225)(115,226)(116,227)(117,222)(118,223)(119,224)(120,237)(121,238)(122,239)(123,243)(124,244)(125,245)(126,240)(127,241)(128,242)(129,228)(130,229)(131,230)(132,234)(133,235)(134,236)(135,231)(136,232)(137,233)(138,246)(139,247)(140,248)(141,252)(142,253)(143,254)(144,249)(145,250)(146,251)(147,264)(148,265)(149,266)(150,270)(151,271)(152,272)(153,267)(154,268)(155,269)(156,255)(157,256)(158,257)(159,261)(160,262)(161,263)(162,258)(163,259)(164,260)(165,273)(166,274)(167,275)(168,279)(169,280)(170,281)(171,276)(172,277)(173,278)(174,291)(175,292)(176,293)(177,297)(178,298)(179,299)(180,294)(181,295)(182,296)(183,282)(184,283)(185,284)(186,288)(187,289)(188,290)(189,285)(190,286)(191,287)(192,300)(193,301)(194,302)(195,306)(196,307)(197,308)(198,303)(199,304)(200,305)(201,318)(202,319)(203,320)(204,324)(205,325)(206,326)(207,321)(208,322)(209,323)(210,309)(211,310)(212,311)(213,315)(214,316)(215,317)(216,312)(217,313)(218,314);; s2 := ( 3,339)( 4,341)( 5,340)( 6,336)( 7,338)( 8,337)( 9,342)( 10,344)( 11,343)( 12,330)( 13,332)( 14,331)( 15,327)( 16,329)( 17,328)( 18,333)( 19,335)( 20,334)( 21,348)( 22,350)( 23,349)( 24,345)( 25,347)( 26,346)( 27,351)( 28,353)( 29,352)( 30,366)( 31,368)( 32,367)( 33,363)( 34,365)( 35,364)( 36,369)( 37,371)( 38,370)( 39,357)( 40,359)( 41,358)( 42,354)( 43,356)( 44,355)( 45,360)( 46,362)( 47,361)( 48,375)( 49,377)( 50,376)( 51,372)( 52,374)( 53,373)( 54,378)( 55,380)( 56,379)( 57,420)( 58,422)( 59,421)( 60,417)( 61,419)( 62,418)( 63,423)( 64,425)( 65,424)( 66,411)( 67,413)( 68,412)( 69,408)( 70,410)( 71,409)( 72,414)( 73,416)( 74,415)( 75,429)( 76,431)( 77,430)( 78,426)( 79,428)( 80,427)( 81,432)( 82,434)( 83,433)( 84,393)( 85,395)( 86,394)( 87,390)( 88,392)( 89,391)( 90,396)( 91,398)( 92,397)( 93,384)( 94,386)( 95,385)( 96,381)( 97,383)( 98,382)( 99,387)(100,389)(101,388)(102,402)(103,404)(104,403)(105,399)(106,401)(107,400)(108,405)(109,407)(110,406)(111,231)(112,233)(113,232)(114,228)(115,230)(116,229)(117,234)(118,236)(119,235)(120,222)(121,224)(122,223)(123,219)(124,221)(125,220)(126,225)(127,227)(128,226)(129,240)(130,242)(131,241)(132,237)(133,239)(134,238)(135,243)(136,245)(137,244)(138,258)(139,260)(140,259)(141,255)(142,257)(143,256)(144,261)(145,263)(146,262)(147,249)(148,251)(149,250)(150,246)(151,248)(152,247)(153,252)(154,254)(155,253)(156,267)(157,269)(158,268)(159,264)(160,266)(161,265)(162,270)(163,272)(164,271)(165,312)(166,314)(167,313)(168,309)(169,311)(170,310)(171,315)(172,317)(173,316)(174,303)(175,305)(176,304)(177,300)(178,302)(179,301)(180,306)(181,308)(182,307)(183,321)(184,323)(185,322)(186,318)(187,320)(188,319)(189,324)(190,326)(191,325)(192,285)(193,287)(194,286)(195,282)(196,284)(197,283)(198,288)(199,290)(200,289)(201,276)(202,278)(203,277)(204,273)(205,275)(206,274)(207,279)(208,281)(209,280)(210,294)(211,296)(212,295)(213,291)(214,293)(215,292)(216,297)(217,299)(218,298);; s3 := ( 3,220)( 4,219)( 5,221)( 6,226)( 7,225)( 8,227)( 9,223)( 10,222)( 11,224)( 12,229)( 13,228)( 14,230)( 15,235)( 16,234)( 17,236)( 18,232)( 19,231)( 20,233)( 21,238)( 22,237)( 23,239)( 24,244)( 25,243)( 26,245)( 27,241)( 28,240)( 29,242)( 30,247)( 31,246)( 32,248)( 33,253)( 34,252)( 35,254)( 36,250)( 37,249)( 38,251)( 39,256)( 40,255)( 41,257)( 42,262)( 43,261)( 44,263)( 45,259)( 46,258)( 47,260)( 48,265)( 49,264)( 50,266)( 51,271)( 52,270)( 53,272)( 54,268)( 55,267)( 56,269)( 57,301)( 58,300)( 59,302)( 60,307)( 61,306)( 62,308)( 63,304)( 64,303)( 65,305)( 66,310)( 67,309)( 68,311)( 69,316)( 70,315)( 71,317)( 72,313)( 73,312)( 74,314)( 75,319)( 76,318)( 77,320)( 78,325)( 79,324)( 80,326)( 81,322)( 82,321)( 83,323)( 84,274)( 85,273)( 86,275)( 87,280)( 88,279)( 89,281)( 90,277)( 91,276)( 92,278)( 93,283)( 94,282)( 95,284)( 96,289)( 97,288)( 98,290)( 99,286)(100,285)(101,287)(102,292)(103,291)(104,293)(105,298)(106,297)(107,299)(108,295)(109,294)(110,296)(111,382)(112,381)(113,383)(114,388)(115,387)(116,389)(117,385)(118,384)(119,386)(120,391)(121,390)(122,392)(123,397)(124,396)(125,398)(126,394)(127,393)(128,395)(129,400)(130,399)(131,401)(132,406)(133,405)(134,407)(135,403)(136,402)(137,404)(138,409)(139,408)(140,410)(141,415)(142,414)(143,416)(144,412)(145,411)(146,413)(147,418)(148,417)(149,419)(150,424)(151,423)(152,425)(153,421)(154,420)(155,422)(156,427)(157,426)(158,428)(159,433)(160,432)(161,434)(162,430)(163,429)(164,431)(165,328)(166,327)(167,329)(168,334)(169,333)(170,335)(171,331)(172,330)(173,332)(174,337)(175,336)(176,338)(177,343)(178,342)(179,344)(180,340)(181,339)(182,341)(183,346)(184,345)(185,347)(186,352)(187,351)(188,353)(189,349)(190,348)(191,350)(192,355)(193,354)(194,356)(195,361)(196,360)(197,362)(198,358)(199,357)(200,359)(201,364)(202,363)(203,365)(204,370)(205,369)(206,371)(207,367)(208,366)(209,368)(210,373)(211,372)(212,374)(213,379)(214,378)(215,380)(216,376)(217,375)(218,377);; 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*s1*s2*s1*s2*s3*s2*s3*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(434)!(1,2); s1 := Sym(434)!( 3,381)( 4,382)( 5,383)( 6,387)( 7,388)( 8,389)( 9,384)( 10,385)( 11,386)( 12,399)( 13,400)( 14,401)( 15,405)( 16,406)( 17,407)( 18,402)( 19,403)( 20,404)( 21,390)( 22,391)( 23,392)( 24,396)( 25,397)( 26,398)( 27,393)( 28,394)( 29,395)( 30,408)( 31,409)( 32,410)( 33,414)( 34,415)( 35,416)( 36,411)( 37,412)( 38,413)( 39,426)( 40,427)( 41,428)( 42,432)( 43,433)( 44,434)( 45,429)( 46,430)( 47,431)( 48,417)( 49,418)( 50,419)( 51,423)( 52,424)( 53,425)( 54,420)( 55,421)( 56,422)( 57,354)( 58,355)( 59,356)( 60,360)( 61,361)( 62,362)( 63,357)( 64,358)( 65,359)( 66,372)( 67,373)( 68,374)( 69,378)( 70,379)( 71,380)( 72,375)( 73,376)( 74,377)( 75,363)( 76,364)( 77,365)( 78,369)( 79,370)( 80,371)( 81,366)( 82,367)( 83,368)( 84,327)( 85,328)( 86,329)( 87,333)( 88,334)( 89,335)( 90,330)( 91,331)( 92,332)( 93,345)( 94,346)( 95,347)( 96,351)( 97,352)( 98,353)( 99,348)(100,349)(101,350)(102,336)(103,337)(104,338)(105,342)(106,343)(107,344)(108,339)(109,340)(110,341)(111,219)(112,220)(113,221)(114,225)(115,226)(116,227)(117,222)(118,223)(119,224)(120,237)(121,238)(122,239)(123,243)(124,244)(125,245)(126,240)(127,241)(128,242)(129,228)(130,229)(131,230)(132,234)(133,235)(134,236)(135,231)(136,232)(137,233)(138,246)(139,247)(140,248)(141,252)(142,253)(143,254)(144,249)(145,250)(146,251)(147,264)(148,265)(149,266)(150,270)(151,271)(152,272)(153,267)(154,268)(155,269)(156,255)(157,256)(158,257)(159,261)(160,262)(161,263)(162,258)(163,259)(164,260)(165,273)(166,274)(167,275)(168,279)(169,280)(170,281)(171,276)(172,277)(173,278)(174,291)(175,292)(176,293)(177,297)(178,298)(179,299)(180,294)(181,295)(182,296)(183,282)(184,283)(185,284)(186,288)(187,289)(188,290)(189,285)(190,286)(191,287)(192,300)(193,301)(194,302)(195,306)(196,307)(197,308)(198,303)(199,304)(200,305)(201,318)(202,319)(203,320)(204,324)(205,325)(206,326)(207,321)(208,322)(209,323)(210,309)(211,310)(212,311)(213,315)(214,316)(215,317)(216,312)(217,313)(218,314); s2 := Sym(434)!( 3,339)( 4,341)( 5,340)( 6,336)( 7,338)( 8,337)( 9,342)( 10,344)( 11,343)( 12,330)( 13,332)( 14,331)( 15,327)( 16,329)( 17,328)( 18,333)( 19,335)( 20,334)( 21,348)( 22,350)( 23,349)( 24,345)( 25,347)( 26,346)( 27,351)( 28,353)( 29,352)( 30,366)( 31,368)( 32,367)( 33,363)( 34,365)( 35,364)( 36,369)( 37,371)( 38,370)( 39,357)( 40,359)( 41,358)( 42,354)( 43,356)( 44,355)( 45,360)( 46,362)( 47,361)( 48,375)( 49,377)( 50,376)( 51,372)( 52,374)( 53,373)( 54,378)( 55,380)( 56,379)( 57,420)( 58,422)( 59,421)( 60,417)( 61,419)( 62,418)( 63,423)( 64,425)( 65,424)( 66,411)( 67,413)( 68,412)( 69,408)( 70,410)( 71,409)( 72,414)( 73,416)( 74,415)( 75,429)( 76,431)( 77,430)( 78,426)( 79,428)( 80,427)( 81,432)( 82,434)( 83,433)( 84,393)( 85,395)( 86,394)( 87,390)( 88,392)( 89,391)( 90,396)( 91,398)( 92,397)( 93,384)( 94,386)( 95,385)( 96,381)( 97,383)( 98,382)( 99,387)(100,389)(101,388)(102,402)(103,404)(104,403)(105,399)(106,401)(107,400)(108,405)(109,407)(110,406)(111,231)(112,233)(113,232)(114,228)(115,230)(116,229)(117,234)(118,236)(119,235)(120,222)(121,224)(122,223)(123,219)(124,221)(125,220)(126,225)(127,227)(128,226)(129,240)(130,242)(131,241)(132,237)(133,239)(134,238)(135,243)(136,245)(137,244)(138,258)(139,260)(140,259)(141,255)(142,257)(143,256)(144,261)(145,263)(146,262)(147,249)(148,251)(149,250)(150,246)(151,248)(152,247)(153,252)(154,254)(155,253)(156,267)(157,269)(158,268)(159,264)(160,266)(161,265)(162,270)(163,272)(164,271)(165,312)(166,314)(167,313)(168,309)(169,311)(170,310)(171,315)(172,317)(173,316)(174,303)(175,305)(176,304)(177,300)(178,302)(179,301)(180,306)(181,308)(182,307)(183,321)(184,323)(185,322)(186,318)(187,320)(188,319)(189,324)(190,326)(191,325)(192,285)(193,287)(194,286)(195,282)(196,284)(197,283)(198,288)(199,290)(200,289)(201,276)(202,278)(203,277)(204,273)(205,275)(206,274)(207,279)(208,281)(209,280)(210,294)(211,296)(212,295)(213,291)(214,293)(215,292)(216,297)(217,299)(218,298); s3 := Sym(434)!( 3,220)( 4,219)( 5,221)( 6,226)( 7,225)( 8,227)( 9,223)( 10,222)( 11,224)( 12,229)( 13,228)( 14,230)( 15,235)( 16,234)( 17,236)( 18,232)( 19,231)( 20,233)( 21,238)( 22,237)( 23,239)( 24,244)( 25,243)( 26,245)( 27,241)( 28,240)( 29,242)( 30,247)( 31,246)( 32,248)( 33,253)( 34,252)( 35,254)( 36,250)( 37,249)( 38,251)( 39,256)( 40,255)( 41,257)( 42,262)( 43,261)( 44,263)( 45,259)( 46,258)( 47,260)( 48,265)( 49,264)( 50,266)( 51,271)( 52,270)( 53,272)( 54,268)( 55,267)( 56,269)( 57,301)( 58,300)( 59,302)( 60,307)( 61,306)( 62,308)( 63,304)( 64,303)( 65,305)( 66,310)( 67,309)( 68,311)( 69,316)( 70,315)( 71,317)( 72,313)( 73,312)( 74,314)( 75,319)( 76,318)( 77,320)( 78,325)( 79,324)( 80,326)( 81,322)( 82,321)( 83,323)( 84,274)( 85,273)( 86,275)( 87,280)( 88,279)( 89,281)( 90,277)( 91,276)( 92,278)( 93,283)( 94,282)( 95,284)( 96,289)( 97,288)( 98,290)( 99,286)(100,285)(101,287)(102,292)(103,291)(104,293)(105,298)(106,297)(107,299)(108,295)(109,294)(110,296)(111,382)(112,381)(113,383)(114,388)(115,387)(116,389)(117,385)(118,384)(119,386)(120,391)(121,390)(122,392)(123,397)(124,396)(125,398)(126,394)(127,393)(128,395)(129,400)(130,399)(131,401)(132,406)(133,405)(134,407)(135,403)(136,402)(137,404)(138,409)(139,408)(140,410)(141,415)(142,414)(143,416)(144,412)(145,411)(146,413)(147,418)(148,417)(149,419)(150,424)(151,423)(152,425)(153,421)(154,420)(155,422)(156,427)(157,426)(158,428)(159,433)(160,432)(161,434)(162,430)(163,429)(164,431)(165,328)(166,327)(167,329)(168,334)(169,333)(170,335)(171,331)(172,330)(173,332)(174,337)(175,336)(176,338)(177,343)(178,342)(179,344)(180,340)(181,339)(182,341)(183,346)(184,345)(185,347)(186,352)(187,351)(188,353)(189,349)(190,348)(191,350)(192,355)(193,354)(194,356)(195,361)(196,360)(197,362)(198,358)(199,357)(200,359)(201,364)(202,363)(203,365)(204,370)(205,369)(206,371)(207,367)(208,366)(209,368)(210,373)(211,372)(212,374)(213,379)(214,378)(215,380)(216,376)(217,375)(218,377); 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*s1*s2*s1*s2*s3*s2*s3*s1*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;