Polytope of Type {24,12} with group SmallGroup(768,1086909)

Overview

Group: SmallGroup(768,1086909)
Rank: 3
Schläfli Type: {24,12}
Vertices, edges, …: 32, 192, 16
Order of s₀s₁s₂: 8
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

{3,3}*24

48-fold

{4,2}*16

96-fold

{2,2}*8

Covers minimal covers in bold

None in this atlas.

Irregular Quotients of which this is a minimal cover

None.

Representations

Permutation Representation (GAP)

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

Permutation Representation (Magma)

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

References