Part of the Atlas of Small Regular Polytopes

Polytope of Type {6,12}

Atlas Canonical Name {6,12}*768j

▶ Play as a twisty puzzle

Overview

Group
SmallGroup(768,1088556)
Rank
3
Schläfli Type
{6,12}
Vertices, edges, …
32, 192, 64
Order of s0s1s2
4
Order of s0s1s2s1
12
Also known as
if this polytope has a name.

Special Properties

  • Compact Hyperbolic Quotient
  • Locally Spherical
  • Orientable

Quotients maximal quotients in bold

2-fold

4-fold

8-fold

16-fold

32-fold

96-fold

Covers minimal covers in bold

None in this atlas.

Irregular Quotients of which this is a minimal cover

Click an entry to reveal its facets and vertex figures.

P/N, where N=<s0*s1*s2*(s1*s0)^2*s2*s1*s0*(s1*s2)^2> of order 2

32 facets

16 vertex figures

P/N, where N=<(s0*s1)^3> of order 2

40 facets

16 vertex figures

P/N, where N=<s1*s2*s1*s0*(s1*s2)^2*s1*s0*s1*s2, s0*s1*s2*(s1*s0)^2*s2*s1*s0*(s1*s2)^2> of order 4

16 facets

8 vertex figures

P/N, where N=<s1*s0*s2*(s1*s0)^2*s1*s2*s1, s0*s1*s0*s2*(s1*s0)^2*s1*s2*s1*s0> of order 4

24 facets

8 vertex figures

P/N, where N=<s0*s1*s2*(s1*s0)^2*s2*s1*s0*(s1*s2)^2, (s1*s0)^2*s2*s1*s0*(s1*s2)^2*s1*s0*s1*s2> of order 4

16 facets

8 vertex figures

Representations

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

References

None.

to this polytope.

Twisty Puzzle