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

Overview

Group: SmallGroup(768,81667)
Rank: 3
Schläfli Type: {4,48}
Vertices, edges, …: 8, 192, 96
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

Quotients maximal quotients in bold

2-fold

3-fold

{4,16}*256a

4-fold

6-fold

8-fold

12-fold

16-fold

24-fold

32-fold

{2,6}*24

48-fold

64-fold

{2,3}*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)^2> of order 2

72 facets

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

4 vertex figures

4 of {48}*96

Representations

Permutation Representation (GAP)

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

Permutation Representation (Magma)

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

References

None.

to this polytope.