Polytope of Type {4,12,8} with group SmallGroup(768,200907)

Overview

Group: SmallGroup(768,200907)
Rank: 4
Schläfli Type: {4,12,8}
Vertices, edges, …: 4, 24, 48, 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

{4,4,8}*256b

4-fold

6-fold

8-fold

12-fold

16-fold

{2,6,2}*48

24-fold

32-fold

{2,3,2}*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

None.

Representations

Permutation Representation (GAP)

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