Polytope of Type {48,4} with group SmallGroup(768,81667)

Overview

Group: SmallGroup(768,81667)
Rank: 3
Schläfli Type: {48,4}
Vertices, edges, …: 96, 192, 8
Order of s₀s₁s₂: 48
Order of s₀s₁s₂s₁: 4
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Orientable
Self-Petrie

Quotients maximal quotients in bold

2-fold

3-fold

{16,4}*256a

4-fold

6-fold

8-fold

12-fold

16-fold

24-fold

32-fold

{6,2}*24

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=<(s1*s2)^2> of order 2

4 facets

4 of {48}*96

72 vertex figures

48 of {2}*4
24 of {4}*8

Representations

Permutation Representation (GAP)

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