Polytope of Type {30,8}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {30,8}*1920g
if this polytope has a name.
Group : SmallGroup(1920,239556)
Rank : 3
Schlafli Type : {30,8}
Number of vertices, edges, etc : 120, 480, 32
Order of s0s1s2 : 120
Order of s0s1s2s1 : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {30,4}*960b
   4-fold quotients : {30,8}*480, {30,4}*480
   5-fold quotients : {6,8}*384g
   8-fold quotients : {30,4}*240a, {15,4}*240, {30,4}*240b, {30,4}*240c
   10-fold quotients : {6,4}*192b
   12-fold quotients : {10,8}*160
   16-fold quotients : {15,4}*120, {30,2}*120
   20-fold quotients : {6,8}*96, {6,4}*96
   24-fold quotients : {10,4}*80
   32-fold quotients : {15,2}*60
   40-fold quotients : {6,4}*48a, {3,4}*48, {6,4}*48b, {6,4}*48c
   48-fold quotients : {10,2}*40
   60-fold quotients : {2,8}*32
   80-fold quotients : {3,4}*24, {6,2}*24
   96-fold quotients : {5,2}*20
   120-fold quotients : {2,4}*16
   160-fold quotients : {3,2}*12
   240-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s0*s1*s2*s1*s0*s2*s1*s2*s1*s2> of order 2.
      16 facets:
         16 of {30}*60
      60 vertex figures:
         60 of {8}*16
   P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1> of order 2.
      16 facets:
         16 of {30}*60
      60 vertex figures:
         60 of {8}*16
   P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1*s2> of order 2.
      16 facets:
         16 of {30}*60
      60 vertex figures:
         60 of {8}*16
   P/N, where N=<s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1> of order 3.
      16 facets:
         8 of {10}*20
         8 of {30}*60
      40 vertex figures:
         40 of {8}*16
   P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1, s0*s1*s0*s1*s2*s1*s0*s1*s2> of order 4.
      8 facets:
         8 of {30}*60
      30 vertex figures:
         30 of {8}*16
   P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1, s1*s0*s2*s1*s2*s1*s0*s2*s1*s2> of order 4.
      8 facets:
         8 of {30}*60
      30 vertex figures:
         30 of {8}*16
   P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1, s0*s1*s0*s2*s1*s2*s1*s0*s2*s1*s2> of order 4.
      8 facets:
         8 of {30}*60
      30 vertex figures:
         30 of {8}*16

Permutation Representation (GAP) : 
s0 := (  3,  4)(  5, 17)(  6, 18)(  7, 20)(  8, 19)(  9, 13)( 10, 14)( 11, 16)( 12, 15)( 21, 41)( 22, 42)( 23, 44)( 24, 43)( 25, 57)( 26, 58)( 27, 60)( 28, 59)( 29, 53)( 30, 54)( 31, 56)( 32, 55)( 33, 49)( 34, 50)( 35, 52)( 36, 51)( 37, 45)( 38, 46)( 39, 48)( 40, 47)( 63, 64)( 65, 77)( 66, 78)( 67, 80)( 68, 79)( 69, 73)( 70, 74)( 71, 76)( 72, 75)( 81,101)( 82,102)( 83,104)( 84,103)( 85,117)( 86,118)( 87,120)( 88,119)( 89,113)( 90,114)( 91,116)( 92,115)( 93,109)( 94,110)( 95,112)( 96,111)( 97,105)( 98,106)( 99,108)(100,107)(123,124)(125,137)(126,138)(127,140)(128,139)(129,133)(130,134)(131,136)(132,135)(141,161)(142,162)(143,164)(144,163)(145,177)(146,178)(147,180)(148,179)(149,173)(150,174)(151,176)(152,175)(153,169)(154,170)(155,172)(156,171)(157,165)(158,166)(159,168)(160,167)(183,184)(185,197)(186,198)(187,200)(188,199)(189,193)(190,194)(191,196)(192,195)(201,221)(202,222)(203,224)(204,223)(205,237)(206,238)(207,240)(208,239)(209,233)(210,234)(211,236)(212,235)(213,229)(214,230)(215,232)(216,231)(217,225)(218,226)(219,228)(220,227)(243,244)(245,257)(246,258)(247,260)(248,259)(249,253)(250,254)(251,256)(252,255)(261,281)(262,282)(263,284)(264,283)(265,297)(266,298)(267,300)(268,299)(269,293)(270,294)(271,296)(272,295)(273,289)(274,290)(275,292)(276,291)(277,285)(278,286)(279,288)(280,287)(303,304)(305,317)(306,318)(307,320)(308,319)(309,313)(310,314)(311,316)(312,315)(321,341)(322,342)(323,344)(324,343)(325,357)(326,358)(327,360)(328,359)(329,353)(330,354)(331,356)(332,355)(333,349)(334,350)(335,352)(336,351)(337,345)(338,346)(339,348)(340,347)(363,364)(365,377)(366,378)(367,380)(368,379)(369,373)(370,374)(371,376)(372,375)(381,401)(382,402)(383,404)(384,403)(385,417)(386,418)(387,420)(388,419)(389,413)(390,414)(391,416)(392,415)(393,409)(394,410)(395,412)(396,411)(397,405)(398,406)(399,408)(400,407)(423,424)(425,437)(426,438)(427,440)(428,439)(429,433)(430,434)(431,436)(432,435)(441,461)(442,462)(443,464)(444,463)(445,477)(446,478)(447,480)(448,479)(449,473)(450,474)(451,476)(452,475)(453,469)(454,470)(455,472)(456,471)(457,465)(458,466)(459,468)(460,467);;
s1 := (  1, 25)(  2, 28)(  3, 27)(  4, 26)(  5, 21)(  6, 24)(  7, 23)(  8, 22)(  9, 37)( 10, 40)( 11, 39)( 12, 38)( 13, 33)( 14, 36)( 15, 35)( 16, 34)( 17, 29)( 18, 32)( 19, 31)( 20, 30)( 41, 45)( 42, 48)( 43, 47)( 44, 46)( 49, 57)( 50, 60)( 51, 59)( 52, 58)( 54, 56)( 61, 85)( 62, 88)( 63, 87)( 64, 86)( 65, 81)( 66, 84)( 67, 83)( 68, 82)( 69, 97)( 70,100)( 71, 99)( 72, 98)( 73, 93)( 74, 96)( 75, 95)( 76, 94)( 77, 89)( 78, 92)( 79, 91)( 80, 90)(101,105)(102,108)(103,107)(104,106)(109,117)(110,120)(111,119)(112,118)(114,116)(121,205)(122,208)(123,207)(124,206)(125,201)(126,204)(127,203)(128,202)(129,217)(130,220)(131,219)(132,218)(133,213)(134,216)(135,215)(136,214)(137,209)(138,212)(139,211)(140,210)(141,185)(142,188)(143,187)(144,186)(145,181)(146,184)(147,183)(148,182)(149,197)(150,200)(151,199)(152,198)(153,193)(154,196)(155,195)(156,194)(157,189)(158,192)(159,191)(160,190)(161,225)(162,228)(163,227)(164,226)(165,221)(166,224)(167,223)(168,222)(169,237)(170,240)(171,239)(172,238)(173,233)(174,236)(175,235)(176,234)(177,229)(178,232)(179,231)(180,230)(241,385)(242,388)(243,387)(244,386)(245,381)(246,384)(247,383)(248,382)(249,397)(250,400)(251,399)(252,398)(253,393)(254,396)(255,395)(256,394)(257,389)(258,392)(259,391)(260,390)(261,365)(262,368)(263,367)(264,366)(265,361)(266,364)(267,363)(268,362)(269,377)(270,380)(271,379)(272,378)(273,373)(274,376)(275,375)(276,374)(277,369)(278,372)(279,371)(280,370)(281,405)(282,408)(283,407)(284,406)(285,401)(286,404)(287,403)(288,402)(289,417)(290,420)(291,419)(292,418)(293,413)(294,416)(295,415)(296,414)(297,409)(298,412)(299,411)(300,410)(301,445)(302,448)(303,447)(304,446)(305,441)(306,444)(307,443)(308,442)(309,457)(310,460)(311,459)(312,458)(313,453)(314,456)(315,455)(316,454)(317,449)(318,452)(319,451)(320,450)(321,425)(322,428)(323,427)(324,426)(325,421)(326,424)(327,423)(328,422)(329,437)(330,440)(331,439)(332,438)(333,433)(334,436)(335,435)(336,434)(337,429)(338,432)(339,431)(340,430)(341,465)(342,468)(343,467)(344,466)(345,461)(346,464)(347,463)(348,462)(349,477)(350,480)(351,479)(352,478)(353,473)(354,476)(355,475)(356,474)(357,469)(358,472)(359,471)(360,470);;
s2 := (  1,242)(  2,241)(  3,244)(  4,243)(  5,246)(  6,245)(  7,248)(  8,247)(  9,250)( 10,249)( 11,252)( 12,251)( 13,254)( 14,253)( 15,256)( 16,255)( 17,258)( 18,257)( 19,260)( 20,259)( 21,262)( 22,261)( 23,264)( 24,263)( 25,266)( 26,265)( 27,268)( 28,267)( 29,270)( 30,269)( 31,272)( 32,271)( 33,274)( 34,273)( 35,276)( 36,275)( 37,278)( 38,277)( 39,280)( 40,279)( 41,282)( 42,281)( 43,284)( 44,283)( 45,286)( 46,285)( 47,288)( 48,287)( 49,290)( 50,289)( 51,292)( 52,291)( 53,294)( 54,293)( 55,296)( 56,295)( 57,298)( 58,297)( 59,300)( 60,299)( 61,302)( 62,301)( 63,304)( 64,303)( 65,306)( 66,305)( 67,308)( 68,307)( 69,310)( 70,309)( 71,312)( 72,311)( 73,314)( 74,313)( 75,316)( 76,315)( 77,318)( 78,317)( 79,320)( 80,319)( 81,322)( 82,321)( 83,324)( 84,323)( 85,326)( 86,325)( 87,328)( 88,327)( 89,330)( 90,329)( 91,332)( 92,331)( 93,334)( 94,333)( 95,336)( 96,335)( 97,338)( 98,337)( 99,340)(100,339)(101,342)(102,341)(103,344)(104,343)(105,346)(106,345)(107,348)(108,347)(109,350)(110,349)(111,352)(112,351)(113,354)(114,353)(115,356)(116,355)(117,358)(118,357)(119,360)(120,359)(121,422)(122,421)(123,424)(124,423)(125,426)(126,425)(127,428)(128,427)(129,430)(130,429)(131,432)(132,431)(133,434)(134,433)(135,436)(136,435)(137,438)(138,437)(139,440)(140,439)(141,442)(142,441)(143,444)(144,443)(145,446)(146,445)(147,448)(148,447)(149,450)(150,449)(151,452)(152,451)(153,454)(154,453)(155,456)(156,455)(157,458)(158,457)(159,460)(160,459)(161,462)(162,461)(163,464)(164,463)(165,466)(166,465)(167,468)(168,467)(169,470)(170,469)(171,472)(172,471)(173,474)(174,473)(175,476)(176,475)(177,478)(178,477)(179,480)(180,479)(181,362)(182,361)(183,364)(184,363)(185,366)(186,365)(187,368)(188,367)(189,370)(190,369)(191,372)(192,371)(193,374)(194,373)(195,376)(196,375)(197,378)(198,377)(199,380)(200,379)(201,382)(202,381)(203,384)(204,383)(205,386)(206,385)(207,388)(208,387)(209,390)(210,389)(211,392)(212,391)(213,394)(214,393)(215,396)(216,395)(217,398)(218,397)(219,400)(220,399)(221,402)(222,401)(223,404)(224,403)(225,406)(226,405)(227,408)(228,407)(229,410)(230,409)(231,412)(232,411)(233,414)(234,413)(235,416)(236,415)(237,418)(238,417)(239,420)(240,419);;
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*s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s0*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 ];;
poly := F / rels;;
Permutation Representation (Magma) : 
s0 := Sym(480)!(  3,  4)(  5, 17)(  6, 18)(  7, 20)(  8, 19)(  9, 13)( 10, 14)( 11, 16)( 12, 15)( 21, 41)( 22, 42)( 23, 44)( 24, 43)( 25, 57)( 26, 58)( 27, 60)( 28, 59)( 29, 53)( 30, 54)( 31, 56)( 32, 55)( 33, 49)( 34, 50)( 35, 52)( 36, 51)( 37, 45)( 38, 46)( 39, 48)( 40, 47)( 63, 64)( 65, 77)( 66, 78)( 67, 80)( 68, 79)( 69, 73)( 70, 74)( 71, 76)( 72, 75)( 81,101)( 82,102)( 83,104)( 84,103)( 85,117)( 86,118)( 87,120)( 88,119)( 89,113)( 90,114)( 91,116)( 92,115)( 93,109)( 94,110)( 95,112)( 96,111)( 97,105)( 98,106)( 99,108)(100,107)(123,124)(125,137)(126,138)(127,140)(128,139)(129,133)(130,134)(131,136)(132,135)(141,161)(142,162)(143,164)(144,163)(145,177)(146,178)(147,180)(148,179)(149,173)(150,174)(151,176)(152,175)(153,169)(154,170)(155,172)(156,171)(157,165)(158,166)(159,168)(160,167)(183,184)(185,197)(186,198)(187,200)(188,199)(189,193)(190,194)(191,196)(192,195)(201,221)(202,222)(203,224)(204,223)(205,237)(206,238)(207,240)(208,239)(209,233)(210,234)(211,236)(212,235)(213,229)(214,230)(215,232)(216,231)(217,225)(218,226)(219,228)(220,227)(243,244)(245,257)(246,258)(247,260)(248,259)(249,253)(250,254)(251,256)(252,255)(261,281)(262,282)(263,284)(264,283)(265,297)(266,298)(267,300)(268,299)(269,293)(270,294)(271,296)(272,295)(273,289)(274,290)(275,292)(276,291)(277,285)(278,286)(279,288)(280,287)(303,304)(305,317)(306,318)(307,320)(308,319)(309,313)(310,314)(311,316)(312,315)(321,341)(322,342)(323,344)(324,343)(325,357)(326,358)(327,360)(328,359)(329,353)(330,354)(331,356)(332,355)(333,349)(334,350)(335,352)(336,351)(337,345)(338,346)(339,348)(340,347)(363,364)(365,377)(366,378)(367,380)(368,379)(369,373)(370,374)(371,376)(372,375)(381,401)(382,402)(383,404)(384,403)(385,417)(386,418)(387,420)(388,419)(389,413)(390,414)(391,416)(392,415)(393,409)(394,410)(395,412)(396,411)(397,405)(398,406)(399,408)(400,407)(423,424)(425,437)(426,438)(427,440)(428,439)(429,433)(430,434)(431,436)(432,435)(441,461)(442,462)(443,464)(444,463)(445,477)(446,478)(447,480)(448,479)(449,473)(450,474)(451,476)(452,475)(453,469)(454,470)(455,472)(456,471)(457,465)(458,466)(459,468)(460,467);
s1 := Sym(480)!(  1, 25)(  2, 28)(  3, 27)(  4, 26)(  5, 21)(  6, 24)(  7, 23)(  8, 22)(  9, 37)( 10, 40)( 11, 39)( 12, 38)( 13, 33)( 14, 36)( 15, 35)( 16, 34)( 17, 29)( 18, 32)( 19, 31)( 20, 30)( 41, 45)( 42, 48)( 43, 47)( 44, 46)( 49, 57)( 50, 60)( 51, 59)( 52, 58)( 54, 56)( 61, 85)( 62, 88)( 63, 87)( 64, 86)( 65, 81)( 66, 84)( 67, 83)( 68, 82)( 69, 97)( 70,100)( 71, 99)( 72, 98)( 73, 93)( 74, 96)( 75, 95)( 76, 94)( 77, 89)( 78, 92)( 79, 91)( 80, 90)(101,105)(102,108)(103,107)(104,106)(109,117)(110,120)(111,119)(112,118)(114,116)(121,205)(122,208)(123,207)(124,206)(125,201)(126,204)(127,203)(128,202)(129,217)(130,220)(131,219)(132,218)(133,213)(134,216)(135,215)(136,214)(137,209)(138,212)(139,211)(140,210)(141,185)(142,188)(143,187)(144,186)(145,181)(146,184)(147,183)(148,182)(149,197)(150,200)(151,199)(152,198)(153,193)(154,196)(155,195)(156,194)(157,189)(158,192)(159,191)(160,190)(161,225)(162,228)(163,227)(164,226)(165,221)(166,224)(167,223)(168,222)(169,237)(170,240)(171,239)(172,238)(173,233)(174,236)(175,235)(176,234)(177,229)(178,232)(179,231)(180,230)(241,385)(242,388)(243,387)(244,386)(245,381)(246,384)(247,383)(248,382)(249,397)(250,400)(251,399)(252,398)(253,393)(254,396)(255,395)(256,394)(257,389)(258,392)(259,391)(260,390)(261,365)(262,368)(263,367)(264,366)(265,361)(266,364)(267,363)(268,362)(269,377)(270,380)(271,379)(272,378)(273,373)(274,376)(275,375)(276,374)(277,369)(278,372)(279,371)(280,370)(281,405)(282,408)(283,407)(284,406)(285,401)(286,404)(287,403)(288,402)(289,417)(290,420)(291,419)(292,418)(293,413)(294,416)(295,415)(296,414)(297,409)(298,412)(299,411)(300,410)(301,445)(302,448)(303,447)(304,446)(305,441)(306,444)(307,443)(308,442)(309,457)(310,460)(311,459)(312,458)(313,453)(314,456)(315,455)(316,454)(317,449)(318,452)(319,451)(320,450)(321,425)(322,428)(323,427)(324,426)(325,421)(326,424)(327,423)(328,422)(329,437)(330,440)(331,439)(332,438)(333,433)(334,436)(335,435)(336,434)(337,429)(338,432)(339,431)(340,430)(341,465)(342,468)(343,467)(344,466)(345,461)(346,464)(347,463)(348,462)(349,477)(350,480)(351,479)(352,478)(353,473)(354,476)(355,475)(356,474)(357,469)(358,472)(359,471)(360,470);
s2 := Sym(480)!(  1,242)(  2,241)(  3,244)(  4,243)(  5,246)(  6,245)(  7,248)(  8,247)(  9,250)( 10,249)( 11,252)( 12,251)( 13,254)( 14,253)( 15,256)( 16,255)( 17,258)( 18,257)( 19,260)( 20,259)( 21,262)( 22,261)( 23,264)( 24,263)( 25,266)( 26,265)( 27,268)( 28,267)( 29,270)( 30,269)( 31,272)( 32,271)( 33,274)( 34,273)( 35,276)( 36,275)( 37,278)( 38,277)( 39,280)( 40,279)( 41,282)( 42,281)( 43,284)( 44,283)( 45,286)( 46,285)( 47,288)( 48,287)( 49,290)( 50,289)( 51,292)( 52,291)( 53,294)( 54,293)( 55,296)( 56,295)( 57,298)( 58,297)( 59,300)( 60,299)( 61,302)( 62,301)( 63,304)( 64,303)( 65,306)( 66,305)( 67,308)( 68,307)( 69,310)( 70,309)( 71,312)( 72,311)( 73,314)( 74,313)( 75,316)( 76,315)( 77,318)( 78,317)( 79,320)( 80,319)( 81,322)( 82,321)( 83,324)( 84,323)( 85,326)( 86,325)( 87,328)( 88,327)( 89,330)( 90,329)( 91,332)( 92,331)( 93,334)( 94,333)( 95,336)( 96,335)( 97,338)( 98,337)( 99,340)(100,339)(101,342)(102,341)(103,344)(104,343)(105,346)(106,345)(107,348)(108,347)(109,350)(110,349)(111,352)(112,351)(113,354)(114,353)(115,356)(116,355)(117,358)(118,357)(119,360)(120,359)(121,422)(122,421)(123,424)(124,423)(125,426)(126,425)(127,428)(128,427)(129,430)(130,429)(131,432)(132,431)(133,434)(134,433)(135,436)(136,435)(137,438)(138,437)(139,440)(140,439)(141,442)(142,441)(143,444)(144,443)(145,446)(146,445)(147,448)(148,447)(149,450)(150,449)(151,452)(152,451)(153,454)(154,453)(155,456)(156,455)(157,458)(158,457)(159,460)(160,459)(161,462)(162,461)(163,464)(164,463)(165,466)(166,465)(167,468)(168,467)(169,470)(170,469)(171,472)(172,471)(173,474)(174,473)(175,476)(176,475)(177,478)(178,477)(179,480)(180,479)(181,362)(182,361)(183,364)(184,363)(185,366)(186,365)(187,368)(188,367)(189,370)(190,369)(191,372)(192,371)(193,374)(194,373)(195,376)(196,375)(197,378)(198,377)(199,380)(200,379)(201,382)(202,381)(203,384)(204,383)(205,386)(206,385)(207,388)(208,387)(209,390)(210,389)(211,392)(212,391)(213,394)(214,393)(215,396)(216,395)(217,398)(218,397)(219,400)(220,399)(221,402)(222,401)(223,404)(224,403)(225,406)(226,405)(227,408)(228,407)(229,410)(230,409)(231,412)(232,411)(233,414)(234,413)(235,416)(236,415)(237,418)(238,417)(239,420)(240,419);
poly := sub<Sym(480)|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*s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s0*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 >;
References : None.
to this polytope

Twisty Puzzle