Part of the Atlas of Small Regular Polytopes

Polytope of Type {38,22}

Atlas Canonical Name {38,22}*1672

▶ Play as a twisty puzzle

Overview

Group
SmallGroup(1672,30)
Rank
3
Schläfli Type
{38,22}
Vertices, edges, …
38, 418, 22
Order of s0s1s2
418
Order of s0s1s2s1
2
Also known as
{38,22|2}. if this polytope has another name.

Special Properties

  • Compact Hyperbolic Quotient
  • Locally Spherical
  • Orientable
  • Flat

Quotients maximal quotients in bold

11-fold

19-fold

22-fold

38-fold

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