Polytope of Type {231,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {231,4}*1848
if this polytope has a name.
Group : SmallGroup(1848,135)
Rank : 3
Schlafli Type : {231,4}
Number of vertices, edges, etc : 231, 462, 4
Order of s0s1s2 : 231
Order of s0s1s2s1 : 4
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Non-Orientable
Flat
Self-Petrie
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Skewing Operation
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
7-fold quotients : {33,4}*264
11-fold quotients : {21,4}*168
77-fold quotients : {3,4}*24
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 3, 4)( 5, 41)( 6, 42)( 7, 44)( 8, 43)( 9, 37)( 10, 38)( 11, 40)
( 12, 39)( 13, 33)( 14, 34)( 15, 36)( 16, 35)( 17, 29)( 18, 30)( 19, 32)
( 20, 31)( 21, 25)( 22, 26)( 23, 28)( 24, 27)( 45,265)( 46,266)( 47,268)
( 48,267)( 49,305)( 50,306)( 51,308)( 52,307)( 53,301)( 54,302)( 55,304)
( 56,303)( 57,297)( 58,298)( 59,300)( 60,299)( 61,293)( 62,294)( 63,296)
( 64,295)( 65,289)( 66,290)( 67,292)( 68,291)( 69,285)( 70,286)( 71,288)
( 72,287)( 73,281)( 74,282)( 75,284)( 76,283)( 77,277)( 78,278)( 79,280)
( 80,279)( 81,273)( 82,274)( 83,276)( 84,275)( 85,269)( 86,270)( 87,272)
( 88,271)( 89,221)( 90,222)( 91,224)( 92,223)( 93,261)( 94,262)( 95,264)
( 96,263)( 97,257)( 98,258)( 99,260)(100,259)(101,253)(102,254)(103,256)
(104,255)(105,249)(106,250)(107,252)(108,251)(109,245)(110,246)(111,248)
(112,247)(113,241)(114,242)(115,244)(116,243)(117,237)(118,238)(119,240)
(120,239)(121,233)(122,234)(123,236)(124,235)(125,229)(126,230)(127,232)
(128,231)(129,225)(130,226)(131,228)(132,227)(133,177)(134,178)(135,180)
(136,179)(137,217)(138,218)(139,220)(140,219)(141,213)(142,214)(143,216)
(144,215)(145,209)(146,210)(147,212)(148,211)(149,205)(150,206)(151,208)
(152,207)(153,201)(154,202)(155,204)(156,203)(157,197)(158,198)(159,200)
(160,199)(161,193)(162,194)(163,196)(164,195)(165,189)(166,190)(167,192)
(168,191)(169,185)(170,186)(171,188)(172,187)(173,181)(174,182)(175,184)
(176,183);;
s1 := ( 1, 49)( 2, 52)( 3, 51)( 4, 50)( 5, 45)( 6, 48)( 7, 47)( 8, 46)
( 9, 85)( 10, 88)( 11, 87)( 12, 86)( 13, 81)( 14, 84)( 15, 83)( 16, 82)
( 17, 77)( 18, 80)( 19, 79)( 20, 78)( 21, 73)( 22, 76)( 23, 75)( 24, 74)
( 25, 69)( 26, 72)( 27, 71)( 28, 70)( 29, 65)( 30, 68)( 31, 67)( 32, 66)
( 33, 61)( 34, 64)( 35, 63)( 36, 62)( 37, 57)( 38, 60)( 39, 59)( 40, 58)
( 41, 53)( 42, 56)( 43, 55)( 44, 54)( 89,269)( 90,272)( 91,271)( 92,270)
( 93,265)( 94,268)( 95,267)( 96,266)( 97,305)( 98,308)( 99,307)(100,306)
(101,301)(102,304)(103,303)(104,302)(105,297)(106,300)(107,299)(108,298)
(109,293)(110,296)(111,295)(112,294)(113,289)(114,292)(115,291)(116,290)
(117,285)(118,288)(119,287)(120,286)(121,281)(122,284)(123,283)(124,282)
(125,277)(126,280)(127,279)(128,278)(129,273)(130,276)(131,275)(132,274)
(133,225)(134,228)(135,227)(136,226)(137,221)(138,224)(139,223)(140,222)
(141,261)(142,264)(143,263)(144,262)(145,257)(146,260)(147,259)(148,258)
(149,253)(150,256)(151,255)(152,254)(153,249)(154,252)(155,251)(156,250)
(157,245)(158,248)(159,247)(160,246)(161,241)(162,244)(163,243)(164,242)
(165,237)(166,240)(167,239)(168,238)(169,233)(170,236)(171,235)(172,234)
(173,229)(174,232)(175,231)(176,230)(177,181)(178,184)(179,183)(180,182)
(185,217)(186,220)(187,219)(188,218)(189,213)(190,216)(191,215)(192,214)
(193,209)(194,212)(195,211)(196,210)(197,205)(198,208)(199,207)(200,206)
(202,204);;
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);;
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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(308)!( 3, 4)( 5, 41)( 6, 42)( 7, 44)( 8, 43)( 9, 37)( 10, 38)
( 11, 40)( 12, 39)( 13, 33)( 14, 34)( 15, 36)( 16, 35)( 17, 29)( 18, 30)
( 19, 32)( 20, 31)( 21, 25)( 22, 26)( 23, 28)( 24, 27)( 45,265)( 46,266)
( 47,268)( 48,267)( 49,305)( 50,306)( 51,308)( 52,307)( 53,301)( 54,302)
( 55,304)( 56,303)( 57,297)( 58,298)( 59,300)( 60,299)( 61,293)( 62,294)
( 63,296)( 64,295)( 65,289)( 66,290)( 67,292)( 68,291)( 69,285)( 70,286)
( 71,288)( 72,287)( 73,281)( 74,282)( 75,284)( 76,283)( 77,277)( 78,278)
( 79,280)( 80,279)( 81,273)( 82,274)( 83,276)( 84,275)( 85,269)( 86,270)
( 87,272)( 88,271)( 89,221)( 90,222)( 91,224)( 92,223)( 93,261)( 94,262)
( 95,264)( 96,263)( 97,257)( 98,258)( 99,260)(100,259)(101,253)(102,254)
(103,256)(104,255)(105,249)(106,250)(107,252)(108,251)(109,245)(110,246)
(111,248)(112,247)(113,241)(114,242)(115,244)(116,243)(117,237)(118,238)
(119,240)(120,239)(121,233)(122,234)(123,236)(124,235)(125,229)(126,230)
(127,232)(128,231)(129,225)(130,226)(131,228)(132,227)(133,177)(134,178)
(135,180)(136,179)(137,217)(138,218)(139,220)(140,219)(141,213)(142,214)
(143,216)(144,215)(145,209)(146,210)(147,212)(148,211)(149,205)(150,206)
(151,208)(152,207)(153,201)(154,202)(155,204)(156,203)(157,197)(158,198)
(159,200)(160,199)(161,193)(162,194)(163,196)(164,195)(165,189)(166,190)
(167,192)(168,191)(169,185)(170,186)(171,188)(172,187)(173,181)(174,182)
(175,184)(176,183);
s1 := Sym(308)!( 1, 49)( 2, 52)( 3, 51)( 4, 50)( 5, 45)( 6, 48)( 7, 47)
( 8, 46)( 9, 85)( 10, 88)( 11, 87)( 12, 86)( 13, 81)( 14, 84)( 15, 83)
( 16, 82)( 17, 77)( 18, 80)( 19, 79)( 20, 78)( 21, 73)( 22, 76)( 23, 75)
( 24, 74)( 25, 69)( 26, 72)( 27, 71)( 28, 70)( 29, 65)( 30, 68)( 31, 67)
( 32, 66)( 33, 61)( 34, 64)( 35, 63)( 36, 62)( 37, 57)( 38, 60)( 39, 59)
( 40, 58)( 41, 53)( 42, 56)( 43, 55)( 44, 54)( 89,269)( 90,272)( 91,271)
( 92,270)( 93,265)( 94,268)( 95,267)( 96,266)( 97,305)( 98,308)( 99,307)
(100,306)(101,301)(102,304)(103,303)(104,302)(105,297)(106,300)(107,299)
(108,298)(109,293)(110,296)(111,295)(112,294)(113,289)(114,292)(115,291)
(116,290)(117,285)(118,288)(119,287)(120,286)(121,281)(122,284)(123,283)
(124,282)(125,277)(126,280)(127,279)(128,278)(129,273)(130,276)(131,275)
(132,274)(133,225)(134,228)(135,227)(136,226)(137,221)(138,224)(139,223)
(140,222)(141,261)(142,264)(143,263)(144,262)(145,257)(146,260)(147,259)
(148,258)(149,253)(150,256)(151,255)(152,254)(153,249)(154,252)(155,251)
(156,250)(157,245)(158,248)(159,247)(160,246)(161,241)(162,244)(163,243)
(164,242)(165,237)(166,240)(167,239)(168,238)(169,233)(170,236)(171,235)
(172,234)(173,229)(174,232)(175,231)(176,230)(177,181)(178,184)(179,183)
(180,182)(185,217)(186,220)(187,219)(188,218)(189,213)(190,216)(191,215)
(192,214)(193,209)(194,212)(195,211)(196,210)(197,205)(198,208)(199,207)
(200,206)(202,204);
s2 := Sym(308)!( 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);
poly := sub<Sym(308)|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 >;
References : None.
to this polytope