Polytope of Type {12,8} with group SmallGroup(768,1086012)

Overview

Group: SmallGroup(768,1086012)
Rank: 3
Schläfli Type: {12,8}
Vertices, edges, …: 48, 192, 32
Order of s₀s₁s₂: 12
Order of s₀s₁s₂s₁: 4
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Non-Orientable
Self-Petrie

Quotients maximal quotients in bold

2-fold

4-fold

{6,4}*192a

8-fold

{12,4}*96b

16-fold

{6,4}*48c

32-fold

{3,4}*24

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*(s2*s1)^2> of order 2

16 facets

16 of {12}*24

24 vertex figures

24 of {8}*16

P/N, where N=<(s0*s1)^2*(s0*s2*s1)^3*s0*s1> of order 2

16 facets

16 of {12}*24

24 vertex figures

24 of {8}*16

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

8 facets

8 of {12}*24

12 vertex figures

12 of {8}*16

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

8 facets

8 of {12}*24

12 vertex figures

12 of {8}*16

Representations

Permutation Representation (GAP)

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

Permutation Representation (Magma)

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

References

None.

to this polytope.