Part of the Atlas of Small Regular Polytopes

Polytope of Type {12,4}

Atlas Canonical Name {12,4}*768h

▶ Play as a twisty puzzle

Overview

Group
SmallGroup(768,1088561)
Rank
3
Schläfli Type
{12,4}
Vertices, edges, …
96, 192, 32
Order of s0s1s2
12
Order of s0s1s2s1
8
Also known as
if this polytope has a name.

Special Properties

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

Quotients maximal quotients in bold

2-fold

4-fold

8-fold

16-fold

32-fold

64-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=<((s1*s0)^2*s1*s2)^2> of order 2

16 facets

48 vertex figures

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

8 facets

24 vertex figures

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

8 facets

24 vertex figures

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

8 facets

24 vertex figures

Representations

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

References

None.

to this polytope.

Twisty Puzzle