Part of the Atlas of Small Regular Polytopes

Polytope of Type {237,4}

Atlas Canonical Name {237,4}*1896

▶ Play as a twisty puzzle

Overview

Group
SmallGroup(1896,43)
Rank
3
Schläfli Type
{237,4}
Vertices, edges, …
237, 474, 4
Order of s0s1s2
237
Order of s0s1s2s1
4
Also known as
if this polytope has a name.

Special Properties

  • Compact Hyperbolic Quotient
  • Locally Spherical
  • Non-Orientable
  • Flat
  • Self-Petrie

Quotients maximal quotients in bold

79-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 := (  3,  4)(  5,313)(  6,314)(  7,316)(  8,315)(  9,309)( 10,310)( 11,312)( 12,311)( 13,305)( 14,306)( 15,308)( 16,307)( 17,301)( 18,302)( 19,304)( 20,303)( 21,297)( 22,298)( 23,300)( 24,299)( 25,293)( 26,294)( 27,296)( 28,295)( 29,289)( 30,290)( 31,292)( 32,291)( 33,285)( 34,286)( 35,288)( 36,287)( 37,281)( 38,282)( 39,284)( 40,283)( 41,277)( 42,278)( 43,280)( 44,279)( 45,273)( 46,274)( 47,276)( 48,275)( 49,269)( 50,270)( 51,272)( 52,271)( 53,265)( 54,266)( 55,268)( 56,267)( 57,261)( 58,262)( 59,264)( 60,263)( 61,257)( 62,258)( 63,260)( 64,259)( 65,253)( 66,254)( 67,256)( 68,255)( 69,249)( 70,250)( 71,252)( 72,251)( 73,245)( 74,246)( 75,248)( 76,247)( 77,241)( 78,242)( 79,244)( 80,243)( 81,237)( 82,238)( 83,240)( 84,239)( 85,233)( 86,234)( 87,236)( 88,235)( 89,229)( 90,230)( 91,232)( 92,231)( 93,225)( 94,226)( 95,228)( 96,227)( 97,221)( 98,222)( 99,224)(100,223)(101,217)(102,218)(103,220)(104,219)(105,213)(106,214)(107,216)(108,215)(109,209)(110,210)(111,212)(112,211)(113,205)(114,206)(115,208)(116,207)(117,201)(118,202)(119,204)(120,203)(121,197)(122,198)(123,200)(124,199)(125,193)(126,194)(127,196)(128,195)(129,189)(130,190)(131,192)(132,191)(133,185)(134,186)(135,188)(136,187)(137,181)(138,182)(139,184)(140,183)(141,177)(142,178)(143,180)(144,179)(145,173)(146,174)(147,176)(148,175)(149,169)(150,170)(151,172)(152,171)(153,165)(154,166)(155,168)(156,167)(157,161)(158,162)(159,164)(160,163);;
s1 := (  1,  5)(  2,  8)(  3,  7)(  4,  6)(  9,313)( 10,316)( 11,315)( 12,314)( 13,309)( 14,312)( 15,311)( 16,310)( 17,305)( 18,308)( 19,307)( 20,306)( 21,301)( 22,304)( 23,303)( 24,302)( 25,297)( 26,300)( 27,299)( 28,298)( 29,293)( 30,296)( 31,295)( 32,294)( 33,289)( 34,292)( 35,291)( 36,290)( 37,285)( 38,288)( 39,287)( 40,286)( 41,281)( 42,284)( 43,283)( 44,282)( 45,277)( 46,280)( 47,279)( 48,278)( 49,273)( 50,276)( 51,275)( 52,274)( 53,269)( 54,272)( 55,271)( 56,270)( 57,265)( 58,268)( 59,267)( 60,266)( 61,261)( 62,264)( 63,263)( 64,262)( 65,257)( 66,260)( 67,259)( 68,258)( 69,253)( 70,256)( 71,255)( 72,254)( 73,249)( 74,252)( 75,251)( 76,250)( 77,245)( 78,248)( 79,247)( 80,246)( 81,241)( 82,244)( 83,243)( 84,242)( 85,237)( 86,240)( 87,239)( 88,238)( 89,233)( 90,236)( 91,235)( 92,234)( 93,229)( 94,232)( 95,231)( 96,230)( 97,225)( 98,228)( 99,227)(100,226)(101,221)(102,224)(103,223)(104,222)(105,217)(106,220)(107,219)(108,218)(109,213)(110,216)(111,215)(112,214)(113,209)(114,212)(115,211)(116,210)(117,205)(118,208)(119,207)(120,206)(121,201)(122,204)(123,203)(124,202)(125,197)(126,200)(127,199)(128,198)(129,193)(130,196)(131,195)(132,194)(133,189)(134,192)(135,191)(136,190)(137,185)(138,188)(139,187)(140,186)(141,181)(142,184)(143,183)(144,182)(145,177)(146,180)(147,179)(148,178)(149,173)(150,176)(151,175)(152,174)(153,169)(154,172)(155,171)(156,170)(157,165)(158,168)(159,167)(160,166)(162,164);;
s2 := (  1,  2)(  3,  4)(  5,  6)(  7,  8)(  9, 10)( 11, 12)( 13, 14)( 15, 16)( 17, 18)( 19, 20)( 21, 22)( 23, 24)( 25, 26)( 27, 28)( 29, 30)( 31, 32)( 33, 34)( 35, 36)( 37, 38)( 39, 40)( 41, 42)( 43, 44)( 45, 46)( 47, 48)( 49, 50)( 51, 52)( 53, 54)( 55, 56)( 57, 58)( 59, 60)( 61, 62)( 63, 64)( 65, 66)( 67, 68)( 69, 70)( 71, 72)( 73, 74)( 75, 76)( 77, 78)( 79, 80)( 81, 82)( 83, 84)( 85, 86)( 87, 88)( 89, 90)( 91, 92)( 93, 94)( 95, 96)( 97, 98)( 99,100)(101,102)(103,104)(105,106)(107,108)(109,110)(111,112)(113,114)(115,116)(117,118)(119,120)(121,122)(123,124)(125,126)(127,128)(129,130)(131,132)(133,134)(135,136)(137,138)(139,140)(141,142)(143,144)(145,146)(147,148)(149,150)(151,152)(153,154)(155,156)(157,158)(159,160)(161,162)(163,164)(165,166)(167,168)(169,170)(171,172)(173,174)(175,176)(177,178)(179,180)(181,182)(183,184)(185,186)(187,188)(189,190)(191,192)(193,194)(195,196)(197,198)(199,200)(201,202)(203,204)(205,206)(207,208)(209,210)(211,212)(213,214)(215,216)(217,218)(219,220)(221,222)(223,224)(225,226)(227,228)(229,230)(231,232)(233,234)(235,236)(237,238)(239,240)(241,242)(243,244)(245,246)(247,248)(249,250)(251,252)(253,254)(255,256)(257,258)(259,260)(261,262)(263,264)(265,266)(267,268)(269,270)(271,272)(273,274)(275,276)(277,278)(279,280)(281,282)(283,284)(285,286)(287,288)(289,290)(291,292)(293,294)(295,296)(297,298)(299,300)(301,302)(303,304)(305,306)(307,308)(309,310)(311,312)(313,314)(315,316);;
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, s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s1*s0*s2*s1*s2*s1*s0*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(316)!(  3,  4)(  5,313)(  6,314)(  7,316)(  8,315)(  9,309)( 10,310)( 11,312)( 12,311)( 13,305)( 14,306)( 15,308)( 16,307)( 17,301)( 18,302)( 19,304)( 20,303)( 21,297)( 22,298)( 23,300)( 24,299)( 25,293)( 26,294)( 27,296)( 28,295)( 29,289)( 30,290)( 31,292)( 32,291)( 33,285)( 34,286)( 35,288)( 36,287)( 37,281)( 38,282)( 39,284)( 40,283)( 41,277)( 42,278)( 43,280)( 44,279)( 45,273)( 46,274)( 47,276)( 48,275)( 49,269)( 50,270)( 51,272)( 52,271)( 53,265)( 54,266)( 55,268)( 56,267)( 57,261)( 58,262)( 59,264)( 60,263)( 61,257)( 62,258)( 63,260)( 64,259)( 65,253)( 66,254)( 67,256)( 68,255)( 69,249)( 70,250)( 71,252)( 72,251)( 73,245)( 74,246)( 75,248)( 76,247)( 77,241)( 78,242)( 79,244)( 80,243)( 81,237)( 82,238)( 83,240)( 84,239)( 85,233)( 86,234)( 87,236)( 88,235)( 89,229)( 90,230)( 91,232)( 92,231)( 93,225)( 94,226)( 95,228)( 96,227)( 97,221)( 98,222)( 99,224)(100,223)(101,217)(102,218)(103,220)(104,219)(105,213)(106,214)(107,216)(108,215)(109,209)(110,210)(111,212)(112,211)(113,205)(114,206)(115,208)(116,207)(117,201)(118,202)(119,204)(120,203)(121,197)(122,198)(123,200)(124,199)(125,193)(126,194)(127,196)(128,195)(129,189)(130,190)(131,192)(132,191)(133,185)(134,186)(135,188)(136,187)(137,181)(138,182)(139,184)(140,183)(141,177)(142,178)(143,180)(144,179)(145,173)(146,174)(147,176)(148,175)(149,169)(150,170)(151,172)(152,171)(153,165)(154,166)(155,168)(156,167)(157,161)(158,162)(159,164)(160,163);
s1 := Sym(316)!(  1,  5)(  2,  8)(  3,  7)(  4,  6)(  9,313)( 10,316)( 11,315)( 12,314)( 13,309)( 14,312)( 15,311)( 16,310)( 17,305)( 18,308)( 19,307)( 20,306)( 21,301)( 22,304)( 23,303)( 24,302)( 25,297)( 26,300)( 27,299)( 28,298)( 29,293)( 30,296)( 31,295)( 32,294)( 33,289)( 34,292)( 35,291)( 36,290)( 37,285)( 38,288)( 39,287)( 40,286)( 41,281)( 42,284)( 43,283)( 44,282)( 45,277)( 46,280)( 47,279)( 48,278)( 49,273)( 50,276)( 51,275)( 52,274)( 53,269)( 54,272)( 55,271)( 56,270)( 57,265)( 58,268)( 59,267)( 60,266)( 61,261)( 62,264)( 63,263)( 64,262)( 65,257)( 66,260)( 67,259)( 68,258)( 69,253)( 70,256)( 71,255)( 72,254)( 73,249)( 74,252)( 75,251)( 76,250)( 77,245)( 78,248)( 79,247)( 80,246)( 81,241)( 82,244)( 83,243)( 84,242)( 85,237)( 86,240)( 87,239)( 88,238)( 89,233)( 90,236)( 91,235)( 92,234)( 93,229)( 94,232)( 95,231)( 96,230)( 97,225)( 98,228)( 99,227)(100,226)(101,221)(102,224)(103,223)(104,222)(105,217)(106,220)(107,219)(108,218)(109,213)(110,216)(111,215)(112,214)(113,209)(114,212)(115,211)(116,210)(117,205)(118,208)(119,207)(120,206)(121,201)(122,204)(123,203)(124,202)(125,197)(126,200)(127,199)(128,198)(129,193)(130,196)(131,195)(132,194)(133,189)(134,192)(135,191)(136,190)(137,185)(138,188)(139,187)(140,186)(141,181)(142,184)(143,183)(144,182)(145,177)(146,180)(147,179)(148,178)(149,173)(150,176)(151,175)(152,174)(153,169)(154,172)(155,171)(156,170)(157,165)(158,168)(159,167)(160,166)(162,164);
s2 := Sym(316)!(  1,  2)(  3,  4)(  5,  6)(  7,  8)(  9, 10)( 11, 12)( 13, 14)( 15, 16)( 17, 18)( 19, 20)( 21, 22)( 23, 24)( 25, 26)( 27, 28)( 29, 30)( 31, 32)( 33, 34)( 35, 36)( 37, 38)( 39, 40)( 41, 42)( 43, 44)( 45, 46)( 47, 48)( 49, 50)( 51, 52)( 53, 54)( 55, 56)( 57, 58)( 59, 60)( 61, 62)( 63, 64)( 65, 66)( 67, 68)( 69, 70)( 71, 72)( 73, 74)( 75, 76)( 77, 78)( 79, 80)( 81, 82)( 83, 84)( 85, 86)( 87, 88)( 89, 90)( 91, 92)( 93, 94)( 95, 96)( 97, 98)( 99,100)(101,102)(103,104)(105,106)(107,108)(109,110)(111,112)(113,114)(115,116)(117,118)(119,120)(121,122)(123,124)(125,126)(127,128)(129,130)(131,132)(133,134)(135,136)(137,138)(139,140)(141,142)(143,144)(145,146)(147,148)(149,150)(151,152)(153,154)(155,156)(157,158)(159,160)(161,162)(163,164)(165,166)(167,168)(169,170)(171,172)(173,174)(175,176)(177,178)(179,180)(181,182)(183,184)(185,186)(187,188)(189,190)(191,192)(193,194)(195,196)(197,198)(199,200)(201,202)(203,204)(205,206)(207,208)(209,210)(211,212)(213,214)(215,216)(217,218)(219,220)(221,222)(223,224)(225,226)(227,228)(229,230)(231,232)(233,234)(235,236)(237,238)(239,240)(241,242)(243,244)(245,246)(247,248)(249,250)(251,252)(253,254)(255,256)(257,258)(259,260)(261,262)(263,264)(265,266)(267,268)(269,270)(271,272)(273,274)(275,276)(277,278)(279,280)(281,282)(283,284)(285,286)(287,288)(289,290)(291,292)(293,294)(295,296)(297,298)(299,300)(301,302)(303,304)(305,306)(307,308)(309,310)(311,312)(313,314)(315,316);
poly := sub<Sym(316)|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, s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s1*s0*s2*s1*s2*s1*s0*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

References

None.

to this polytope.

Twisty Puzzle