Polytope of Type {12,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,4}*768e
if this polytope has a name.
Group : SmallGroup(768,1087779)
Rank : 3
Schlafli Type : {12,4}
Number of vertices, edges, etc : 96, 192, 32
Order of s₀s₁s₂ : 24
Order of s₀s₁s₂s₁ : 8
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {12,4}*384d, {12,4}*384e, {6,4}*384b
   4-fold quotients : {12,4}*192b, {6,4}*192b, {12,4}*192c
   8-fold quotients : {12,4}*96a, {12,4}*96b, {12,4}*96c, {6,4}*96
   16-fold quotients : {12,2}*48, {6,4}*48a, {3,4}*48, {6,4}*48b, {6,4}*48c
   24-fold quotients : {4,4}*32
   32-fold quotients : {3,4}*24, {6,2}*24
   48-fold quotients : {2,4}*16, {4,2}*16
   64-fold quotients : {3,2}*12
   96-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope