Polytope of Type {6,8,4} with group SmallGroup(768,141629)

Overview

Group: SmallGroup(768,141629)
Rank: 4
Schläfli Type: {6,8,4}
Vertices, edges, …: 6, 48, 32, 8
Order of s₀s₁s₂s₃: 24
Order of s₀s₁s₂s₃s₂s₁: 2
Also known as: if this polytope has a name.

Special Properties

Universal
Orientable
Flat

Quotients maximal quotients in bold

2-fold

3-fold

{2,8,4}*256a

4-fold

6-fold

8-fold

12-fold

16-fold

24-fold

32-fold

{3,2,2}*24

48-fold

{2,2,2}*16

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=<(s2*s3)^2> of order 2

4 facets

4 of {6,8}*96

6 vertex figures

6 of 2-fold non-regular quotient of {8,4}*128a

Representations

Permutation Representation (GAP)

s0 := (  1, 49)(  2, 51)(  3, 50)(  4, 52)(  5, 54)(  6, 53)(  7, 55)(  8, 57)(  9, 56)( 10, 58)( 11, 60)( 12, 59)( 13, 61)( 14, 63)( 15, 62)( 16, 64)( 17, 66)( 18, 65)( 19, 67)( 20, 69)( 21, 68)( 22, 70)( 23, 72)( 24, 71)( 25, 73)( 26, 75)( 27, 74)( 28, 76)( 29, 78)( 30, 77)( 31, 79)( 32, 81)( 33, 80)( 34, 82)( 35, 84)( 36, 83)( 37, 85)( 38, 87)( 39, 86)( 40, 88)( 41, 90)( 42, 89)( 43, 91)( 44, 93)( 45, 92)( 46, 94)( 47, 96)( 48, 95)( 97,145)( 98,147)( 99,146)(100,148)(101,150)(102,149)(103,151)(104,153)(105,152)(106,154)(107,156)(108,155)(109,157)(110,159)(111,158)(112,160)(113,162)(114,161)(115,163)(116,165)(117,164)(118,166)(119,168)(120,167)(121,169)(122,171)(123,170)(124,172)(125,174)(126,173)(127,175)(128,177)(129,176)(130,178)(131,180)(132,179)(133,181)(134,183)(135,182)(136,184)(137,186)(138,185)(139,187)(140,189)(141,188)(142,190)(143,192)(144,191)(193,241)(194,243)(195,242)(196,244)(197,246)(198,245)(199,247)(200,249)(201,248)(202,250)(203,252)(204,251)(205,253)(206,255)(207,254)(208,256)(209,258)(210,257)(211,259)(212,261)(213,260)(214,262)(215,264)(216,263)(217,265)(218,267)(219,266)(220,268)(221,270)(222,269)(223,271)(224,273)(225,272)(226,274)(227,276)(228,275)(229,277)(230,279)(231,278)(232,280)(233,282)(234,281)(235,283)(236,285)(237,284)(238,286)(239,288)(240,287)(289,337)(290,339)(291,338)(292,340)(293,342)(294,341)(295,343)(296,345)(297,344)(298,346)(299,348)(300,347)(301,349)(302,351)(303,350)(304,352)(305,354)(306,353)(307,355)(308,357)(309,356)(310,358)(311,360)(312,359)(313,361)(314,363)(315,362)(316,364)(317,366)(318,365)(319,367)(320,369)(321,368)(322,370)(323,372)(324,371)(325,373)(326,375)(327,374)(328,376)(329,378)(330,377)(331,379)(332,381)(333,380)(334,382)(335,384)(336,383);;
s1 := (  1,243)(  2,242)(  3,241)(  4,246)(  5,245)(  6,244)(  7,249)(  8,248)(  9,247)( 10,252)( 11,251)( 12,250)( 13,258)( 14,257)( 15,256)( 16,255)( 17,254)( 18,253)( 19,264)( 20,263)( 21,262)( 22,261)( 23,260)( 24,259)( 25,273)( 26,272)( 27,271)( 28,276)( 29,275)( 30,274)( 31,267)( 32,266)( 33,265)( 34,270)( 35,269)( 36,268)( 37,288)( 38,287)( 39,286)( 40,285)( 41,284)( 42,283)( 43,282)( 44,281)( 45,280)( 46,279)( 47,278)( 48,277)( 49,195)( 50,194)( 51,193)( 52,198)( 53,197)( 54,196)( 55,201)( 56,200)( 57,199)( 58,204)( 59,203)( 60,202)( 61,210)( 62,209)( 63,208)( 64,207)( 65,206)( 66,205)( 67,216)( 68,215)( 69,214)( 70,213)( 71,212)( 72,211)( 73,225)( 74,224)( 75,223)( 76,228)( 77,227)( 78,226)( 79,219)( 80,218)( 81,217)( 82,222)( 83,221)( 84,220)( 85,240)( 86,239)( 87,238)( 88,237)( 89,236)( 90,235)( 91,234)( 92,233)( 93,232)( 94,231)( 95,230)( 96,229)( 97,339)( 98,338)( 99,337)(100,342)(101,341)(102,340)(103,345)(104,344)(105,343)(106,348)(107,347)(108,346)(109,354)(110,353)(111,352)(112,351)(113,350)(114,349)(115,360)(116,359)(117,358)(118,357)(119,356)(120,355)(121,369)(122,368)(123,367)(124,372)(125,371)(126,370)(127,363)(128,362)(129,361)(130,366)(131,365)(132,364)(133,384)(134,383)(135,382)(136,381)(137,380)(138,379)(139,378)(140,377)(141,376)(142,375)(143,374)(144,373)(145,291)(146,290)(147,289)(148,294)(149,293)(150,292)(151,297)(152,296)(153,295)(154,300)(155,299)(156,298)(157,306)(158,305)(159,304)(160,303)(161,302)(162,301)(163,312)(164,311)(165,310)(166,309)(167,308)(168,307)(169,321)(170,320)(171,319)(172,324)(173,323)(174,322)(175,315)(176,314)(177,313)(178,318)(179,317)(180,316)(181,336)(182,335)(183,334)(184,333)(185,332)(186,331)(187,330)(188,329)(189,328)(190,327)(191,326)(192,325);;
s2 := ( 25, 31)( 26, 32)( 27, 33)( 28, 34)( 29, 35)( 30, 36)( 37, 43)( 38, 44)( 39, 45)( 40, 46)( 41, 47)( 42, 48)( 73, 79)( 74, 80)( 75, 81)( 76, 82)( 77, 83)( 78, 84)( 85, 91)( 86, 92)( 87, 93)( 88, 94)( 89, 95)( 90, 96)( 97,109)( 98,110)( 99,111)(100,112)(101,113)(102,114)(103,115)(104,116)(105,117)(106,118)(107,119)(108,120)(121,139)(122,140)(123,141)(124,142)(125,143)(126,144)(127,133)(128,134)(129,135)(130,136)(131,137)(132,138)(145,157)(146,158)(147,159)(148,160)(149,161)(150,162)(151,163)(152,164)(153,165)(154,166)(155,167)(156,168)(169,187)(170,188)(171,189)(172,190)(173,191)(174,192)(175,181)(176,182)(177,183)(178,184)(179,185)(180,186)(193,217)(194,218)(195,219)(196,220)(197,221)(198,222)(199,223)(200,224)(201,225)(202,226)(203,227)(204,228)(205,229)(206,230)(207,231)(208,232)(209,233)(210,234)(211,235)(212,236)(213,237)(214,238)(215,239)(216,240)(241,265)(242,266)(243,267)(244,268)(245,269)(246,270)(247,271)(248,272)(249,273)(250,274)(251,275)(252,276)(253,277)(254,278)(255,279)(256,280)(257,281)(258,282)(259,283)(260,284)(261,285)(262,286)(263,287)(264,288)(289,328)(290,329)(291,330)(292,325)(293,326)(294,327)(295,334)(296,335)(297,336)(298,331)(299,332)(300,333)(301,316)(302,317)(303,318)(304,313)(305,314)(306,315)(307,322)(308,323)(309,324)(310,319)(311,320)(312,321)(337,376)(338,377)(339,378)(340,373)(341,374)(342,375)(343,382)(344,383)(345,384)(346,379)(347,380)(348,381)(349,364)(350,365)(351,366)(352,361)(353,362)(354,363)(355,370)(356,371)(357,372)(358,367)(359,368)(360,369);;
s3 := (  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)( 25,124)( 26,125)( 27,126)( 28,121)( 29,122)( 30,123)( 31,130)( 32,131)( 33,132)( 34,127)( 35,128)( 36,129)( 37,136)( 38,137)( 39,138)( 40,133)( 41,134)( 42,135)( 43,142)( 44,143)( 45,144)( 46,139)( 47,140)( 48,141)( 49,145)( 50,146)( 51,147)( 52,148)( 53,149)( 54,150)( 55,151)( 56,152)( 57,153)( 58,154)( 59,155)( 60,156)( 61,157)( 62,158)( 63,159)( 64,160)( 65,161)( 66,162)( 67,163)( 68,164)( 69,165)( 70,166)( 71,167)( 72,168)( 73,172)( 74,173)( 75,174)( 76,169)( 77,170)( 78,171)( 79,178)( 80,179)( 81,180)( 82,175)( 83,176)( 84,177)( 85,184)( 86,185)( 87,186)( 88,181)( 89,182)( 90,183)( 91,190)( 92,191)( 93,192)( 94,187)( 95,188)( 96,189)(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)(217,316)(218,317)(219,318)(220,313)(221,314)(222,315)(223,322)(224,323)(225,324)(226,319)(227,320)(228,321)(229,328)(230,329)(231,330)(232,325)(233,326)(234,327)(235,334)(236,335)(237,336)(238,331)(239,332)(240,333)(241,337)(242,338)(243,339)(244,340)(245,341)(246,342)(247,343)(248,344)(249,345)(250,346)(251,347)(252,348)(253,349)(254,350)(255,351)(256,352)(257,353)(258,354)(259,355)(260,356)(261,357)(262,358)(263,359)(264,360)(265,364)(266,365)(267,366)(268,361)(269,362)(270,363)(271,370)(272,371)(273,372)(274,367)(275,368)(276,369)(277,376)(278,377)(279,378)(280,373)(281,374)(282,375)(283,382)(284,383)(285,384)(286,379)(287,380)(288,381);;
poly := Group([s0,s1,s2,s3]);;

Finitely Presented Group Representation (GAP)

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s1*s2*s1*s0*s1*s2*s1, 
s2*s3*s2*s3*s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s3*s2*s3*s2*s1*s2*s1*s3*s2*s3*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, 49)(  2, 51)(  3, 50)(  4, 52)(  5, 54)(  6, 53)(  7, 55)(  8, 57)(  9, 56)( 10, 58)( 11, 60)( 12, 59)( 13, 61)( 14, 63)( 15, 62)( 16, 64)( 17, 66)( 18, 65)( 19, 67)( 20, 69)( 21, 68)( 22, 70)( 23, 72)( 24, 71)( 25, 73)( 26, 75)( 27, 74)( 28, 76)( 29, 78)( 30, 77)( 31, 79)( 32, 81)( 33, 80)( 34, 82)( 35, 84)( 36, 83)( 37, 85)( 38, 87)( 39, 86)( 40, 88)( 41, 90)( 42, 89)( 43, 91)( 44, 93)( 45, 92)( 46, 94)( 47, 96)( 48, 95)( 97,145)( 98,147)( 99,146)(100,148)(101,150)(102,149)(103,151)(104,153)(105,152)(106,154)(107,156)(108,155)(109,157)(110,159)(111,158)(112,160)(113,162)(114,161)(115,163)(116,165)(117,164)(118,166)(119,168)(120,167)(121,169)(122,171)(123,170)(124,172)(125,174)(126,173)(127,175)(128,177)(129,176)(130,178)(131,180)(132,179)(133,181)(134,183)(135,182)(136,184)(137,186)(138,185)(139,187)(140,189)(141,188)(142,190)(143,192)(144,191)(193,241)(194,243)(195,242)(196,244)(197,246)(198,245)(199,247)(200,249)(201,248)(202,250)(203,252)(204,251)(205,253)(206,255)(207,254)(208,256)(209,258)(210,257)(211,259)(212,261)(213,260)(214,262)(215,264)(216,263)(217,265)(218,267)(219,266)(220,268)(221,270)(222,269)(223,271)(224,273)(225,272)(226,274)(227,276)(228,275)(229,277)(230,279)(231,278)(232,280)(233,282)(234,281)(235,283)(236,285)(237,284)(238,286)(239,288)(240,287)(289,337)(290,339)(291,338)(292,340)(293,342)(294,341)(295,343)(296,345)(297,344)(298,346)(299,348)(300,347)(301,349)(302,351)(303,350)(304,352)(305,354)(306,353)(307,355)(308,357)(309,356)(310,358)(311,360)(312,359)(313,361)(314,363)(315,362)(316,364)(317,366)(318,365)(319,367)(320,369)(321,368)(322,370)(323,372)(324,371)(325,373)(326,375)(327,374)(328,376)(329,378)(330,377)(331,379)(332,381)(333,380)(334,382)(335,384)(336,383);
s1 := Sym(384)!(  1,243)(  2,242)(  3,241)(  4,246)(  5,245)(  6,244)(  7,249)(  8,248)(  9,247)( 10,252)( 11,251)( 12,250)( 13,258)( 14,257)( 15,256)( 16,255)( 17,254)( 18,253)( 19,264)( 20,263)( 21,262)( 22,261)( 23,260)( 24,259)( 25,273)( 26,272)( 27,271)( 28,276)( 29,275)( 30,274)( 31,267)( 32,266)( 33,265)( 34,270)( 35,269)( 36,268)( 37,288)( 38,287)( 39,286)( 40,285)( 41,284)( 42,283)( 43,282)( 44,281)( 45,280)( 46,279)( 47,278)( 48,277)( 49,195)( 50,194)( 51,193)( 52,198)( 53,197)( 54,196)( 55,201)( 56,200)( 57,199)( 58,204)( 59,203)( 60,202)( 61,210)( 62,209)( 63,208)( 64,207)( 65,206)( 66,205)( 67,216)( 68,215)( 69,214)( 70,213)( 71,212)( 72,211)( 73,225)( 74,224)( 75,223)( 76,228)( 77,227)( 78,226)( 79,219)( 80,218)( 81,217)( 82,222)( 83,221)( 84,220)( 85,240)( 86,239)( 87,238)( 88,237)( 89,236)( 90,235)( 91,234)( 92,233)( 93,232)( 94,231)( 95,230)( 96,229)( 97,339)( 98,338)( 99,337)(100,342)(101,341)(102,340)(103,345)(104,344)(105,343)(106,348)(107,347)(108,346)(109,354)(110,353)(111,352)(112,351)(113,350)(114,349)(115,360)(116,359)(117,358)(118,357)(119,356)(120,355)(121,369)(122,368)(123,367)(124,372)(125,371)(126,370)(127,363)(128,362)(129,361)(130,366)(131,365)(132,364)(133,384)(134,383)(135,382)(136,381)(137,380)(138,379)(139,378)(140,377)(141,376)(142,375)(143,374)(144,373)(145,291)(146,290)(147,289)(148,294)(149,293)(150,292)(151,297)(152,296)(153,295)(154,300)(155,299)(156,298)(157,306)(158,305)(159,304)(160,303)(161,302)(162,301)(163,312)(164,311)(165,310)(166,309)(167,308)(168,307)(169,321)(170,320)(171,319)(172,324)(173,323)(174,322)(175,315)(176,314)(177,313)(178,318)(179,317)(180,316)(181,336)(182,335)(183,334)(184,333)(185,332)(186,331)(187,330)(188,329)(189,328)(190,327)(191,326)(192,325);
s2 := Sym(384)!( 25, 31)( 26, 32)( 27, 33)( 28, 34)( 29, 35)( 30, 36)( 37, 43)( 38, 44)( 39, 45)( 40, 46)( 41, 47)( 42, 48)( 73, 79)( 74, 80)( 75, 81)( 76, 82)( 77, 83)( 78, 84)( 85, 91)( 86, 92)( 87, 93)( 88, 94)( 89, 95)( 90, 96)( 97,109)( 98,110)( 99,111)(100,112)(101,113)(102,114)(103,115)(104,116)(105,117)(106,118)(107,119)(108,120)(121,139)(122,140)(123,141)(124,142)(125,143)(126,144)(127,133)(128,134)(129,135)(130,136)(131,137)(132,138)(145,157)(146,158)(147,159)(148,160)(149,161)(150,162)(151,163)(152,164)(153,165)(154,166)(155,167)(156,168)(169,187)(170,188)(171,189)(172,190)(173,191)(174,192)(175,181)(176,182)(177,183)(178,184)(179,185)(180,186)(193,217)(194,218)(195,219)(196,220)(197,221)(198,222)(199,223)(200,224)(201,225)(202,226)(203,227)(204,228)(205,229)(206,230)(207,231)(208,232)(209,233)(210,234)(211,235)(212,236)(213,237)(214,238)(215,239)(216,240)(241,265)(242,266)(243,267)(244,268)(245,269)(246,270)(247,271)(248,272)(249,273)(250,274)(251,275)(252,276)(253,277)(254,278)(255,279)(256,280)(257,281)(258,282)(259,283)(260,284)(261,285)(262,286)(263,287)(264,288)(289,328)(290,329)(291,330)(292,325)(293,326)(294,327)(295,334)(296,335)(297,336)(298,331)(299,332)(300,333)(301,316)(302,317)(303,318)(304,313)(305,314)(306,315)(307,322)(308,323)(309,324)(310,319)(311,320)(312,321)(337,376)(338,377)(339,378)(340,373)(341,374)(342,375)(343,382)(344,383)(345,384)(346,379)(347,380)(348,381)(349,364)(350,365)(351,366)(352,361)(353,362)(354,363)(355,370)(356,371)(357,372)(358,367)(359,368)(360,369);
s3 := 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)( 25,124)( 26,125)( 27,126)( 28,121)( 29,122)( 30,123)( 31,130)( 32,131)( 33,132)( 34,127)( 35,128)( 36,129)( 37,136)( 38,137)( 39,138)( 40,133)( 41,134)( 42,135)( 43,142)( 44,143)( 45,144)( 46,139)( 47,140)( 48,141)( 49,145)( 50,146)( 51,147)( 52,148)( 53,149)( 54,150)( 55,151)( 56,152)( 57,153)( 58,154)( 59,155)( 60,156)( 61,157)( 62,158)( 63,159)( 64,160)( 65,161)( 66,162)( 67,163)( 68,164)( 69,165)( 70,166)( 71,167)( 72,168)( 73,172)( 74,173)( 75,174)( 76,169)( 77,170)( 78,171)( 79,178)( 80,179)( 81,180)( 82,175)( 83,176)( 84,177)( 85,184)( 86,185)( 87,186)( 88,181)( 89,182)( 90,183)( 91,190)( 92,191)( 93,192)( 94,187)( 95,188)( 96,189)(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)(217,316)(218,317)(219,318)(220,313)(221,314)(222,315)(223,322)(224,323)(225,324)(226,319)(227,320)(228,321)(229,328)(230,329)(231,330)(232,325)(233,326)(234,327)(235,334)(236,335)(237,336)(238,331)(239,332)(240,333)(241,337)(242,338)(243,339)(244,340)(245,341)(246,342)(247,343)(248,344)(249,345)(250,346)(251,347)(252,348)(253,349)(254,350)(255,351)(256,352)(257,353)(258,354)(259,355)(260,356)(261,357)(262,358)(263,359)(264,360)(265,364)(266,365)(267,366)(268,361)(269,362)(270,363)(271,370)(272,371)(273,372)(274,367)(275,368)(276,369)(277,376)(278,377)(279,378)(280,373)(281,374)(282,375)(283,382)(284,383)(285,384)(286,379)(287,380)(288,381);
poly := sub<Sym(384)|s0,s1,s2,s3>;

Finitely Presented Group Representation (Magma)

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s1*s2*s1*s0*s1*s2*s1, s2*s3*s2*s3*s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s3*s2*s3*s2*s1*s2*s1*s3*s2*s3*s2*s1*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

References

None.

to this polytope.