Polytope of Type {24,4} with group SmallGroup(768,1087779)

Overview

Group: SmallGroup(768,1087779)
Rank: 3
Schläfli Type: {24,4}
Vertices, edges, …: 96, 192, 16
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

Quotients maximal quotients in bold

2-fold

4-fold

8-fold

16-fold

24-fold

{4,4}*32

32-fold

48-fold

64-fold

{3,2}*12

96-fold

{2,2}*8

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)^3*(s0*s2*s1)^3*s2> of order 2

8 facets

8 of {24}*48

48 vertex figures

48 of {4}*8

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

8 facets

4 of {8}*16
4 of {24}*48

32 vertex figures

32 of {4}*8

Representations

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*s1*s0*s2*s1*s2*s1*s0*s1*s0*s1*s0*s2*s1*s2*s1*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*s2*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*s1*s0*s2*s1*s2*s1*s0*s1*s0*s1*s0*s2*s1*s2*s1*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*s2*s0*s1 >;

References

None.

to this polytope.