Polytope of Type {24,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24,4}*768k
if this polytope has a name.
Group : SmallGroup(768,1087779)
Rank : 3
Schlafli Type : {24,4}
Number of vertices, edges, etc : 96, 192, 16
Order of s0s1s2 : 12
Order of s0s1s2s1 : 8
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Skewing Operation
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {12,4}*384d, {24,4}*384e, {24,4}*384f
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 := ( 3, 4)( 5, 7)( 6, 8)( 9, 17)( 10, 18)( 11, 20)( 12, 19)( 13, 23)
( 14, 24)( 15, 21)( 16, 22)( 25, 26)( 29, 32)( 30, 31)( 33, 42)( 34, 41)
( 35, 43)( 36, 44)( 37, 48)( 38, 47)( 39, 46)( 40, 45)( 49, 50)( 53, 56)
( 54, 55)( 57, 66)( 58, 65)( 59, 67)( 60, 68)( 61, 72)( 62, 71)( 63, 70)
( 64, 69)( 75, 76)( 77, 79)( 78, 80)( 81, 89)( 82, 90)( 83, 92)( 84, 91)
( 85, 95)( 86, 96)( 87, 93)( 88, 94)( 97,121)( 98,122)( 99,124)(100,123)
(101,127)(102,128)(103,125)(104,126)(105,137)(106,138)(107,140)(108,139)
(109,143)(110,144)(111,141)(112,142)(113,129)(114,130)(115,132)(116,131)
(117,135)(118,136)(119,133)(120,134)(145,170)(146,169)(147,171)(148,172)
(149,176)(150,175)(151,174)(152,173)(153,186)(154,185)(155,187)(156,188)
(157,192)(158,191)(159,190)(160,189)(161,178)(162,177)(163,179)(164,180)
(165,184)(166,183)(167,182)(168,181)(195,196)(197,199)(198,200)(201,209)
(202,210)(203,212)(204,211)(205,215)(206,216)(207,213)(208,214)(217,218)
(221,224)(222,223)(225,234)(226,233)(227,235)(228,236)(229,240)(230,239)
(231,238)(232,237)(241,242)(245,248)(246,247)(249,258)(250,257)(251,259)
(252,260)(253,264)(254,263)(255,262)(256,261)(267,268)(269,271)(270,272)
(273,281)(274,282)(275,284)(276,283)(277,287)(278,288)(279,285)(280,286)
(289,313)(290,314)(291,316)(292,315)(293,319)(294,320)(295,317)(296,318)
(297,329)(298,330)(299,332)(300,331)(301,335)(302,336)(303,333)(304,334)
(305,321)(306,322)(307,324)(308,323)(309,327)(310,328)(311,325)(312,326)
(337,362)(338,361)(339,363)(340,364)(341,368)(342,367)(343,366)(344,365)
(345,378)(346,377)(347,379)(348,380)(349,384)(350,383)(351,382)(352,381)
(353,370)(354,369)(355,371)(356,372)(357,376)(358,375)(359,374)(360,373);;
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 := ( 1,243)( 2,244)( 3,242)( 4,241)( 5,247)( 6,248)( 7,246)( 8,245)
( 9,251)( 10,252)( 11,250)( 12,249)( 13,255)( 14,256)( 15,254)( 16,253)
( 17,259)( 18,260)( 19,258)( 20,257)( 21,263)( 22,264)( 23,262)( 24,261)
( 25,268)( 26,267)( 27,265)( 28,266)( 29,272)( 30,271)( 31,269)( 32,270)
( 33,276)( 34,275)( 35,273)( 36,274)( 37,280)( 38,279)( 39,277)( 40,278)
( 41,284)( 42,283)( 43,281)( 44,282)( 45,288)( 46,287)( 47,285)( 48,286)
( 49,195)( 50,196)( 51,194)( 52,193)( 53,199)( 54,200)( 55,198)( 56,197)
( 57,203)( 58,204)( 59,202)( 60,201)( 61,207)( 62,208)( 63,206)( 64,205)
( 65,211)( 66,212)( 67,210)( 68,209)( 69,215)( 70,216)( 71,214)( 72,213)
( 73,220)( 74,219)( 75,217)( 76,218)( 77,224)( 78,223)( 79,221)( 80,222)
( 81,228)( 82,227)( 83,225)( 84,226)( 85,232)( 86,231)( 87,229)( 88,230)
( 89,236)( 90,235)( 91,233)( 92,234)( 93,240)( 94,239)( 95,237)( 96,238)
( 97,292)( 98,291)( 99,289)(100,290)(101,296)(102,295)(103,293)(104,294)
(105,300)(106,299)(107,297)(108,298)(109,304)(110,303)(111,301)(112,302)
(113,308)(114,307)(115,305)(116,306)(117,312)(118,311)(119,309)(120,310)
(121,315)(122,316)(123,314)(124,313)(125,319)(126,320)(127,318)(128,317)
(129,323)(130,324)(131,322)(132,321)(133,327)(134,328)(135,326)(136,325)
(137,331)(138,332)(139,330)(140,329)(141,335)(142,336)(143,334)(144,333)
(145,339)(146,340)(147,338)(148,337)(149,343)(150,344)(151,342)(152,341)
(153,347)(154,348)(155,346)(156,345)(157,351)(158,352)(159,350)(160,349)
(161,355)(162,356)(163,354)(164,353)(165,359)(166,360)(167,358)(168,357)
(169,364)(170,363)(171,361)(172,362)(173,368)(174,367)(175,365)(176,366)
(177,372)(178,371)(179,369)(180,370)(181,376)(182,375)(183,373)(184,374)
(185,380)(186,379)(187,377)(188,378)(189,384)(190,383)(191,381)(192,382);;
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*s2*s1*s2*s1*s0*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1*s0*s1,
s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(384)!( 3, 4)( 5, 7)( 6, 8)( 9, 17)( 10, 18)( 11, 20)( 12, 19)
( 13, 23)( 14, 24)( 15, 21)( 16, 22)( 25, 26)( 29, 32)( 30, 31)( 33, 42)
( 34, 41)( 35, 43)( 36, 44)( 37, 48)( 38, 47)( 39, 46)( 40, 45)( 49, 50)
( 53, 56)( 54, 55)( 57, 66)( 58, 65)( 59, 67)( 60, 68)( 61, 72)( 62, 71)
( 63, 70)( 64, 69)( 75, 76)( 77, 79)( 78, 80)( 81, 89)( 82, 90)( 83, 92)
( 84, 91)( 85, 95)( 86, 96)( 87, 93)( 88, 94)( 97,121)( 98,122)( 99,124)
(100,123)(101,127)(102,128)(103,125)(104,126)(105,137)(106,138)(107,140)
(108,139)(109,143)(110,144)(111,141)(112,142)(113,129)(114,130)(115,132)
(116,131)(117,135)(118,136)(119,133)(120,134)(145,170)(146,169)(147,171)
(148,172)(149,176)(150,175)(151,174)(152,173)(153,186)(154,185)(155,187)
(156,188)(157,192)(158,191)(159,190)(160,189)(161,178)(162,177)(163,179)
(164,180)(165,184)(166,183)(167,182)(168,181)(195,196)(197,199)(198,200)
(201,209)(202,210)(203,212)(204,211)(205,215)(206,216)(207,213)(208,214)
(217,218)(221,224)(222,223)(225,234)(226,233)(227,235)(228,236)(229,240)
(230,239)(231,238)(232,237)(241,242)(245,248)(246,247)(249,258)(250,257)
(251,259)(252,260)(253,264)(254,263)(255,262)(256,261)(267,268)(269,271)
(270,272)(273,281)(274,282)(275,284)(276,283)(277,287)(278,288)(279,285)
(280,286)(289,313)(290,314)(291,316)(292,315)(293,319)(294,320)(295,317)
(296,318)(297,329)(298,330)(299,332)(300,331)(301,335)(302,336)(303,333)
(304,334)(305,321)(306,322)(307,324)(308,323)(309,327)(310,328)(311,325)
(312,326)(337,362)(338,361)(339,363)(340,364)(341,368)(342,367)(343,366)
(344,365)(345,378)(346,377)(347,379)(348,380)(349,384)(350,383)(351,382)
(352,381)(353,370)(354,369)(355,371)(356,372)(357,376)(358,375)(359,374)
(360,373);
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)!( 1,243)( 2,244)( 3,242)( 4,241)( 5,247)( 6,248)( 7,246)
( 8,245)( 9,251)( 10,252)( 11,250)( 12,249)( 13,255)( 14,256)( 15,254)
( 16,253)( 17,259)( 18,260)( 19,258)( 20,257)( 21,263)( 22,264)( 23,262)
( 24,261)( 25,268)( 26,267)( 27,265)( 28,266)( 29,272)( 30,271)( 31,269)
( 32,270)( 33,276)( 34,275)( 35,273)( 36,274)( 37,280)( 38,279)( 39,277)
( 40,278)( 41,284)( 42,283)( 43,281)( 44,282)( 45,288)( 46,287)( 47,285)
( 48,286)( 49,195)( 50,196)( 51,194)( 52,193)( 53,199)( 54,200)( 55,198)
( 56,197)( 57,203)( 58,204)( 59,202)( 60,201)( 61,207)( 62,208)( 63,206)
( 64,205)( 65,211)( 66,212)( 67,210)( 68,209)( 69,215)( 70,216)( 71,214)
( 72,213)( 73,220)( 74,219)( 75,217)( 76,218)( 77,224)( 78,223)( 79,221)
( 80,222)( 81,228)( 82,227)( 83,225)( 84,226)( 85,232)( 86,231)( 87,229)
( 88,230)( 89,236)( 90,235)( 91,233)( 92,234)( 93,240)( 94,239)( 95,237)
( 96,238)( 97,292)( 98,291)( 99,289)(100,290)(101,296)(102,295)(103,293)
(104,294)(105,300)(106,299)(107,297)(108,298)(109,304)(110,303)(111,301)
(112,302)(113,308)(114,307)(115,305)(116,306)(117,312)(118,311)(119,309)
(120,310)(121,315)(122,316)(123,314)(124,313)(125,319)(126,320)(127,318)
(128,317)(129,323)(130,324)(131,322)(132,321)(133,327)(134,328)(135,326)
(136,325)(137,331)(138,332)(139,330)(140,329)(141,335)(142,336)(143,334)
(144,333)(145,339)(146,340)(147,338)(148,337)(149,343)(150,344)(151,342)
(152,341)(153,347)(154,348)(155,346)(156,345)(157,351)(158,352)(159,350)
(160,349)(161,355)(162,356)(163,354)(164,353)(165,359)(166,360)(167,358)
(168,357)(169,364)(170,363)(171,361)(172,362)(173,368)(174,367)(175,365)
(176,366)(177,372)(178,371)(179,369)(180,370)(181,376)(182,375)(183,373)
(184,374)(185,380)(186,379)(187,377)(188,378)(189,384)(190,383)(191,381)
(192,382);
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*s2*s1*s2*s1*s0*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1*s0*s1,
s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope