Polytope of Type {3,24} with group SmallGroup(768,1085768)

Overview

Group: SmallGroup(768,1085768)
Rank: 3
Schläfli Type: {3,24}
Vertices, edges, …: 16, 192, 128
Order of s₀s₁s₂: 16
Order of s₀s₁s₂s₁: 24
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Orientable

Quotients maximal quotients in bold

2-fold

{3,12}*384

4-fold

{3,6}*192

8-fold

{3,12}*96

16-fold

{3,6}*48

32-fold

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

64 facets

64 of {3}*6

8 vertex figures

8 of {24}*48

P/N, where N=<s1*s0*(s2*s1)^3*s0*(s2*s1)^2*s2, s1*s2*s1*s0*(s2*s1)^3*s0*s2*s1*s2> of order 4

32 facets

32 of {3}*6

4 vertex figures

4 of {24}*48

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

32 facets

32 of {3}*6

4 vertex figures

4 of {24}*48

Representations

Permutation Representation (GAP)

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

Permutation Representation (Magma)

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

References

None.

to this polytope.