Polytope of Type {4,12,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,12,4}*768h
if this polytope has a name.
Group : SmallGroup(768,1088921)
Rank : 4
Schlafli Type : {4,12,4}
Number of vertices, edges, etc : 8, 48, 48, 4
Order of s0s1s2s3 : 12
Order of s0s1s2s3s2s1 : 2
Special Properties :
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {4,6,4}*384b, {4,12,2}*384c
4-fold quotients : {4,6,4}*192c, {4,6,2}*192
8-fold quotients : {2,6,4}*96a, {4,3,2}*96, {4,6,2}*96b, {4,6,2}*96c
16-fold quotients : {4,3,2}*48, {2,6,2}*48
24-fold quotients : {2,2,4}*32
32-fold quotients : {2,3,2}*24
48-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
Irregular Quotients (of which this is a minimal cover):
P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s1*s2> of order 2.
4 facets:
4 of 2-fold non-regular quotient of {4,12}*192c
4 vertex figures:
4 of {12,4}*96a
P/N, where N=<s0*s1*s0*s1> of order 2.
4 facets:
4 of 2-fold non-regular quotient of {4,12}*192c
4 vertex figures:
4 of {12,4}*96a
Permutation Representation (GAP) :
s0 := ( 1,196)( 2,195)( 3,194)( 4,193)( 5,200)( 6,199)( 7,198)( 8,197)( 9,204)( 10,203)( 11,202)( 12,201)( 13,208)( 14,207)( 15,206)( 16,205)( 17,212)( 18,211)( 19,210)( 20,209)( 21,216)( 22,215)( 23,214)( 24,213)( 25,220)( 26,219)( 27,218)( 28,217)( 29,224)( 30,223)( 31,222)( 32,221)( 33,228)( 34,227)( 35,226)( 36,225)( 37,232)( 38,231)( 39,230)( 40,229)( 41,236)( 42,235)( 43,234)( 44,233)( 45,240)( 46,239)( 47,238)( 48,237)( 49,256)( 50,255)( 51,254)( 52,253)( 53,260)( 54,259)( 55,258)( 56,257)( 57,264)( 58,263)( 59,262)( 60,261)( 61,244)( 62,243)( 63,242)( 64,241)( 65,248)( 66,247)( 67,246)( 68,245)( 69,252)( 70,251)( 71,250)( 72,249)( 73,280)( 74,279)( 75,278)( 76,277)( 77,284)( 78,283)( 79,282)( 80,281)( 81,288)( 82,287)( 83,286)( 84,285)( 85,268)( 86,267)( 87,266)( 88,265)( 89,272)( 90,271)( 91,270)( 92,269)( 93,276)( 94,275)( 95,274)( 96,273)( 97,292)( 98,291)( 99,290)(100,289)(101,296)(102,295)(103,294)(104,293)(105,300)(106,299)(107,298)(108,297)(109,304)(110,303)(111,302)(112,301)(113,308)(114,307)(115,306)(116,305)(117,312)(118,311)(119,310)(120,309)(121,316)(122,315)(123,314)(124,313)(125,320)(126,319)(127,318)(128,317)(129,324)(130,323)(131,322)(132,321)(133,328)(134,327)(135,326)(136,325)(137,332)(138,331)(139,330)(140,329)(141,336)(142,335)(143,334)(144,333)(145,352)(146,351)(147,350)(148,349)(149,356)(150,355)(151,354)(152,353)(153,360)(154,359)(155,358)(156,357)(157,340)(158,339)(159,338)(160,337)(161,344)(162,343)(163,342)(164,341)(165,348)(166,347)(167,346)(168,345)(169,376)(170,375)(171,374)(172,373)(173,380)(174,379)(175,378)(176,377)(177,384)(178,383)(179,382)(180,381)(181,364)(182,363)(183,362)(184,361)(185,368)(186,367)(187,366)(188,365)(189,372)(190,371)(191,370)(192,369);;
s1 := ( 3, 4)( 5, 9)( 6, 10)( 7, 12)( 8, 11)( 15, 16)( 17, 21)( 18, 22)( 19, 24)( 20, 23)( 27, 28)( 29, 33)( 30, 34)( 31, 36)( 32, 35)( 39, 40)( 41, 45)( 42, 46)( 43, 48)( 44, 47)( 51, 52)( 53, 57)( 54, 58)( 55, 60)( 56, 59)( 63, 64)( 65, 69)( 66, 70)( 67, 72)( 68, 71)( 75, 76)( 77, 81)( 78, 82)( 79, 84)( 80, 83)( 87, 88)( 89, 93)( 90, 94)( 91, 96)( 92, 95)( 99,100)(101,105)(102,106)(103,108)(104,107)(111,112)(113,117)(114,118)(115,120)(116,119)(123,124)(125,129)(126,130)(127,132)(128,131)(135,136)(137,141)(138,142)(139,144)(140,143)(147,148)(149,153)(150,154)(151,156)(152,155)(159,160)(161,165)(162,166)(163,168)(164,167)(171,172)(173,177)(174,178)(175,180)(176,179)(183,184)(185,189)(186,190)(187,192)(188,191)(193,205)(194,206)(195,208)(196,207)(197,213)(198,214)(199,216)(200,215)(201,209)(202,210)(203,212)(204,211)(217,229)(218,230)(219,232)(220,231)(221,237)(222,238)(223,240)(224,239)(225,233)(226,234)(227,236)(228,235)(241,253)(242,254)(243,256)(244,255)(245,261)(246,262)(247,264)(248,263)(249,257)(250,258)(251,260)(252,259)(265,277)(266,278)(267,280)(268,279)(269,285)(270,286)(271,288)(272,287)(273,281)(274,282)(275,284)(276,283)(289,301)(290,302)(291,304)(292,303)(293,309)(294,310)(295,312)(296,311)(297,305)(298,306)(299,308)(300,307)(313,325)(314,326)(315,328)(316,327)(317,333)(318,334)(319,336)(320,335)(321,329)(322,330)(323,332)(324,331)(337,349)(338,350)(339,352)(340,351)(341,357)(342,358)(343,360)(344,359)(345,353)(346,354)(347,356)(348,355)(361,373)(362,374)(363,376)(364,375)(365,381)(366,382)(367,384)(368,383)(369,377)(370,378)(371,380)(372,379);;
s2 := ( 1,249)( 2,251)( 3,250)( 4,252)( 5,245)( 6,247)( 7,246)( 8,248)( 9,241)( 10,243)( 11,242)( 12,244)( 13,261)( 14,263)( 15,262)( 16,264)( 17,257)( 18,259)( 19,258)( 20,260)( 21,253)( 22,255)( 23,254)( 24,256)( 25,273)( 26,275)( 27,274)( 28,276)( 29,269)( 30,271)( 31,270)( 32,272)( 33,265)( 34,267)( 35,266)( 36,268)( 37,285)( 38,287)( 39,286)( 40,288)( 41,281)( 42,283)( 43,282)( 44,284)( 45,277)( 46,279)( 47,278)( 48,280)( 49,213)( 50,215)( 51,214)( 52,216)( 53,209)( 54,211)( 55,210)( 56,212)( 57,205)( 58,207)( 59,206)( 60,208)( 61,201)( 62,203)( 63,202)( 64,204)( 65,197)( 66,199)( 67,198)( 68,200)( 69,193)( 70,195)( 71,194)( 72,196)( 73,237)( 74,239)( 75,238)( 76,240)( 77,233)( 78,235)( 79,234)( 80,236)( 81,229)( 82,231)( 83,230)( 84,232)( 85,225)( 86,227)( 87,226)( 88,228)( 89,221)( 90,223)( 91,222)( 92,224)( 93,217)( 94,219)( 95,218)( 96,220)( 97,345)( 98,347)( 99,346)(100,348)(101,341)(102,343)(103,342)(104,344)(105,337)(106,339)(107,338)(108,340)(109,357)(110,359)(111,358)(112,360)(113,353)(114,355)(115,354)(116,356)(117,349)(118,351)(119,350)(120,352)(121,369)(122,371)(123,370)(124,372)(125,365)(126,367)(127,366)(128,368)(129,361)(130,363)(131,362)(132,364)(133,381)(134,383)(135,382)(136,384)(137,377)(138,379)(139,378)(140,380)(141,373)(142,375)(143,374)(144,376)(145,309)(146,311)(147,310)(148,312)(149,305)(150,307)(151,306)(152,308)(153,301)(154,303)(155,302)(156,304)(157,297)(158,299)(159,298)(160,300)(161,293)(162,295)(163,294)(164,296)(165,289)(166,291)(167,290)(168,292)(169,333)(170,335)(171,334)(172,336)(173,329)(174,331)(175,330)(176,332)(177,325)(178,327)(179,326)(180,328)(181,321)(182,323)(183,322)(184,324)(185,317)(186,319)(187,318)(188,320)(189,313)(190,315)(191,314)(192,316);;
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)( 25,121)( 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)( 49,169)( 50,170)( 51,171)( 52,172)( 53,173)( 54,174)( 55,175)( 56,176)( 57,177)( 58,178)( 59,179)( 60,180)( 61,181)( 62,182)( 63,183)( 64,184)( 65,185)( 66,186)( 67,187)( 68,188)( 69,189)( 70,190)( 71,191)( 72,192)( 73,145)( 74,146)( 75,147)( 76,148)( 77,149)( 78,150)( 79,151)( 80,152)( 81,153)( 82,154)( 83,155)( 84,156)( 85,157)( 86,158)( 87,159)( 88,160)( 89,161)( 90,162)( 91,163)( 92,164)( 93,165)( 94,166)( 95,167)( 96,168)(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)(241,361)(242,362)(243,363)(244,364)(245,365)(246,366)(247,367)(248,368)(249,369)(250,370)(251,371)(252,372)(253,373)(254,374)(255,375)(256,376)(257,377)(258,378)(259,379)(260,380)(261,381)(262,382)(263,383)(264,384)(265,337)(266,338)(267,339)(268,340)(269,341)(270,342)(271,343)(272,344)(273,345)(274,346)(275,347)(276,348)(277,349)(278,350)(279,351)(280,352)(281,353)(282,354)(283,355)(284,356)(285,357)(286,358)(287,359)(288,360);;
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,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3,
s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(384)!( 1,196)( 2,195)( 3,194)( 4,193)( 5,200)( 6,199)( 7,198)( 8,197)( 9,204)( 10,203)( 11,202)( 12,201)( 13,208)( 14,207)( 15,206)( 16,205)( 17,212)( 18,211)( 19,210)( 20,209)( 21,216)( 22,215)( 23,214)( 24,213)( 25,220)( 26,219)( 27,218)( 28,217)( 29,224)( 30,223)( 31,222)( 32,221)( 33,228)( 34,227)( 35,226)( 36,225)( 37,232)( 38,231)( 39,230)( 40,229)( 41,236)( 42,235)( 43,234)( 44,233)( 45,240)( 46,239)( 47,238)( 48,237)( 49,256)( 50,255)( 51,254)( 52,253)( 53,260)( 54,259)( 55,258)( 56,257)( 57,264)( 58,263)( 59,262)( 60,261)( 61,244)( 62,243)( 63,242)( 64,241)( 65,248)( 66,247)( 67,246)( 68,245)( 69,252)( 70,251)( 71,250)( 72,249)( 73,280)( 74,279)( 75,278)( 76,277)( 77,284)( 78,283)( 79,282)( 80,281)( 81,288)( 82,287)( 83,286)( 84,285)( 85,268)( 86,267)( 87,266)( 88,265)( 89,272)( 90,271)( 91,270)( 92,269)( 93,276)( 94,275)( 95,274)( 96,273)( 97,292)( 98,291)( 99,290)(100,289)(101,296)(102,295)(103,294)(104,293)(105,300)(106,299)(107,298)(108,297)(109,304)(110,303)(111,302)(112,301)(113,308)(114,307)(115,306)(116,305)(117,312)(118,311)(119,310)(120,309)(121,316)(122,315)(123,314)(124,313)(125,320)(126,319)(127,318)(128,317)(129,324)(130,323)(131,322)(132,321)(133,328)(134,327)(135,326)(136,325)(137,332)(138,331)(139,330)(140,329)(141,336)(142,335)(143,334)(144,333)(145,352)(146,351)(147,350)(148,349)(149,356)(150,355)(151,354)(152,353)(153,360)(154,359)(155,358)(156,357)(157,340)(158,339)(159,338)(160,337)(161,344)(162,343)(163,342)(164,341)(165,348)(166,347)(167,346)(168,345)(169,376)(170,375)(171,374)(172,373)(173,380)(174,379)(175,378)(176,377)(177,384)(178,383)(179,382)(180,381)(181,364)(182,363)(183,362)(184,361)(185,368)(186,367)(187,366)(188,365)(189,372)(190,371)(191,370)(192,369);
s1 := Sym(384)!( 3, 4)( 5, 9)( 6, 10)( 7, 12)( 8, 11)( 15, 16)( 17, 21)( 18, 22)( 19, 24)( 20, 23)( 27, 28)( 29, 33)( 30, 34)( 31, 36)( 32, 35)( 39, 40)( 41, 45)( 42, 46)( 43, 48)( 44, 47)( 51, 52)( 53, 57)( 54, 58)( 55, 60)( 56, 59)( 63, 64)( 65, 69)( 66, 70)( 67, 72)( 68, 71)( 75, 76)( 77, 81)( 78, 82)( 79, 84)( 80, 83)( 87, 88)( 89, 93)( 90, 94)( 91, 96)( 92, 95)( 99,100)(101,105)(102,106)(103,108)(104,107)(111,112)(113,117)(114,118)(115,120)(116,119)(123,124)(125,129)(126,130)(127,132)(128,131)(135,136)(137,141)(138,142)(139,144)(140,143)(147,148)(149,153)(150,154)(151,156)(152,155)(159,160)(161,165)(162,166)(163,168)(164,167)(171,172)(173,177)(174,178)(175,180)(176,179)(183,184)(185,189)(186,190)(187,192)(188,191)(193,205)(194,206)(195,208)(196,207)(197,213)(198,214)(199,216)(200,215)(201,209)(202,210)(203,212)(204,211)(217,229)(218,230)(219,232)(220,231)(221,237)(222,238)(223,240)(224,239)(225,233)(226,234)(227,236)(228,235)(241,253)(242,254)(243,256)(244,255)(245,261)(246,262)(247,264)(248,263)(249,257)(250,258)(251,260)(252,259)(265,277)(266,278)(267,280)(268,279)(269,285)(270,286)(271,288)(272,287)(273,281)(274,282)(275,284)(276,283)(289,301)(290,302)(291,304)(292,303)(293,309)(294,310)(295,312)(296,311)(297,305)(298,306)(299,308)(300,307)(313,325)(314,326)(315,328)(316,327)(317,333)(318,334)(319,336)(320,335)(321,329)(322,330)(323,332)(324,331)(337,349)(338,350)(339,352)(340,351)(341,357)(342,358)(343,360)(344,359)(345,353)(346,354)(347,356)(348,355)(361,373)(362,374)(363,376)(364,375)(365,381)(366,382)(367,384)(368,383)(369,377)(370,378)(371,380)(372,379);
s2 := Sym(384)!( 1,249)( 2,251)( 3,250)( 4,252)( 5,245)( 6,247)( 7,246)( 8,248)( 9,241)( 10,243)( 11,242)( 12,244)( 13,261)( 14,263)( 15,262)( 16,264)( 17,257)( 18,259)( 19,258)( 20,260)( 21,253)( 22,255)( 23,254)( 24,256)( 25,273)( 26,275)( 27,274)( 28,276)( 29,269)( 30,271)( 31,270)( 32,272)( 33,265)( 34,267)( 35,266)( 36,268)( 37,285)( 38,287)( 39,286)( 40,288)( 41,281)( 42,283)( 43,282)( 44,284)( 45,277)( 46,279)( 47,278)( 48,280)( 49,213)( 50,215)( 51,214)( 52,216)( 53,209)( 54,211)( 55,210)( 56,212)( 57,205)( 58,207)( 59,206)( 60,208)( 61,201)( 62,203)( 63,202)( 64,204)( 65,197)( 66,199)( 67,198)( 68,200)( 69,193)( 70,195)( 71,194)( 72,196)( 73,237)( 74,239)( 75,238)( 76,240)( 77,233)( 78,235)( 79,234)( 80,236)( 81,229)( 82,231)( 83,230)( 84,232)( 85,225)( 86,227)( 87,226)( 88,228)( 89,221)( 90,223)( 91,222)( 92,224)( 93,217)( 94,219)( 95,218)( 96,220)( 97,345)( 98,347)( 99,346)(100,348)(101,341)(102,343)(103,342)(104,344)(105,337)(106,339)(107,338)(108,340)(109,357)(110,359)(111,358)(112,360)(113,353)(114,355)(115,354)(116,356)(117,349)(118,351)(119,350)(120,352)(121,369)(122,371)(123,370)(124,372)(125,365)(126,367)(127,366)(128,368)(129,361)(130,363)(131,362)(132,364)(133,381)(134,383)(135,382)(136,384)(137,377)(138,379)(139,378)(140,380)(141,373)(142,375)(143,374)(144,376)(145,309)(146,311)(147,310)(148,312)(149,305)(150,307)(151,306)(152,308)(153,301)(154,303)(155,302)(156,304)(157,297)(158,299)(159,298)(160,300)(161,293)(162,295)(163,294)(164,296)(165,289)(166,291)(167,290)(168,292)(169,333)(170,335)(171,334)(172,336)(173,329)(174,331)(175,330)(176,332)(177,325)(178,327)(179,326)(180,328)(181,321)(182,323)(183,322)(184,324)(185,317)(186,319)(187,318)(188,320)(189,313)(190,315)(191,314)(192,316);
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)( 25,121)( 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)( 49,169)( 50,170)( 51,171)( 52,172)( 53,173)( 54,174)( 55,175)( 56,176)( 57,177)( 58,178)( 59,179)( 60,180)( 61,181)( 62,182)( 63,183)( 64,184)( 65,185)( 66,186)( 67,187)( 68,188)( 69,189)( 70,190)( 71,191)( 72,192)( 73,145)( 74,146)( 75,147)( 76,148)( 77,149)( 78,150)( 79,151)( 80,152)( 81,153)( 82,154)( 83,155)( 84,156)( 85,157)( 86,158)( 87,159)( 88,160)( 89,161)( 90,162)( 91,163)( 92,164)( 93,165)( 94,166)( 95,167)( 96,168)(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)(241,361)(242,362)(243,363)(244,364)(245,365)(246,366)(247,367)(248,368)(249,369)(250,370)(251,371)(252,372)(253,373)(254,374)(255,375)(256,376)(257,377)(258,378)(259,379)(260,380)(261,381)(262,382)(263,383)(264,384)(265,337)(266,338)(267,339)(268,340)(269,341)(270,342)(271,343)(272,344)(273,345)(274,346)(275,347)(276,348)(277,349)(278,350)(279,351)(280,352)(281,353)(282,354)(283,355)(284,356)(285,357)(286,358)(287,359)(288,360);
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, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3, s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1 >;
References : None.
to this polytope