Polytope of Type {3,4,6,3}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,4,6,3}*1152
Also Known As : {{3,4},{4,6|2},{6,3}4}. if this polytope has another name.
Group : SmallGroup(1152,157851)
Rank : 5
Schlafli Type : {3,4,6,3}
Number of vertices, edges, etc : 6, 12, 32, 12, 4
Order of s0s1s2s3s4 : 12
Order of s0s1s2s3s4s3s2s1 : 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) :
4-fold quotients : {3,2,6,3}*288
8-fold quotients : {3,2,3,3}*144
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 3, 4)( 7, 8)( 11, 12)( 15, 16)( 19, 20)( 23, 24)( 27, 28)( 31, 32)
( 35, 36)( 39, 40)( 43, 44)( 47, 48)( 49, 97)( 50, 98)( 51,100)( 52, 99)
( 53,101)( 54,102)( 55,104)( 56,103)( 57,105)( 58,106)( 59,108)( 60,107)
( 61,109)( 62,110)( 63,112)( 64,111)( 65,113)( 66,114)( 67,116)( 68,115)
( 69,117)( 70,118)( 71,120)( 72,119)( 73,121)( 74,122)( 75,124)( 76,123)
( 77,125)( 78,126)( 79,128)( 80,127)( 81,129)( 82,130)( 83,132)( 84,131)
( 85,133)( 86,134)( 87,136)( 88,135)( 89,137)( 90,138)( 91,140)( 92,139)
( 93,141)( 94,142)( 95,144)( 96,143)(147,148)(151,152)(155,156)(159,160)
(163,164)(167,168)(171,172)(175,176)(179,180)(183,184)(187,188)(191,192)
(193,241)(194,242)(195,244)(196,243)(197,245)(198,246)(199,248)(200,247)
(201,249)(202,250)(203,252)(204,251)(205,253)(206,254)(207,256)(208,255)
(209,257)(210,258)(211,260)(212,259)(213,261)(214,262)(215,264)(216,263)
(217,265)(218,266)(219,268)(220,267)(221,269)(222,270)(223,272)(224,271)
(225,273)(226,274)(227,276)(228,275)(229,277)(230,278)(231,280)(232,279)
(233,281)(234,282)(235,284)(236,283)(237,285)(238,286)(239,288)(240,287);;
s1 := ( 1, 49)( 2, 52)( 3, 51)( 4, 50)( 5, 53)( 6, 56)( 7, 55)( 8, 54)
( 9, 57)( 10, 60)( 11, 59)( 12, 58)( 13, 61)( 14, 64)( 15, 63)( 16, 62)
( 17, 65)( 18, 68)( 19, 67)( 20, 66)( 21, 69)( 22, 72)( 23, 71)( 24, 70)
( 25, 73)( 26, 76)( 27, 75)( 28, 74)( 29, 77)( 30, 80)( 31, 79)( 32, 78)
( 33, 81)( 34, 84)( 35, 83)( 36, 82)( 37, 85)( 38, 88)( 39, 87)( 40, 86)
( 41, 89)( 42, 92)( 43, 91)( 44, 90)( 45, 93)( 46, 96)( 47, 95)( 48, 94)
( 98,100)(102,104)(106,108)(110,112)(114,116)(118,120)(122,124)(126,128)
(130,132)(134,136)(138,140)(142,144)(145,193)(146,196)(147,195)(148,194)
(149,197)(150,200)(151,199)(152,198)(153,201)(154,204)(155,203)(156,202)
(157,205)(158,208)(159,207)(160,206)(161,209)(162,212)(163,211)(164,210)
(165,213)(166,216)(167,215)(168,214)(169,217)(170,220)(171,219)(172,218)
(173,221)(174,224)(175,223)(176,222)(177,225)(178,228)(179,227)(180,226)
(181,229)(182,232)(183,231)(184,230)(185,233)(186,236)(187,235)(188,234)
(189,237)(190,240)(191,239)(192,238)(242,244)(246,248)(250,252)(254,256)
(258,260)(262,264)(266,268)(270,272)(274,276)(278,280)(282,284)(286,288);;
s2 := ( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9, 14)( 10, 13)( 11, 16)( 12, 15)
( 17, 34)( 18, 33)( 19, 36)( 20, 35)( 21, 38)( 22, 37)( 23, 40)( 24, 39)
( 25, 46)( 26, 45)( 27, 48)( 28, 47)( 29, 42)( 30, 41)( 31, 44)( 32, 43)
( 49, 50)( 51, 52)( 53, 54)( 55, 56)( 57, 62)( 58, 61)( 59, 64)( 60, 63)
( 65, 82)( 66, 81)( 67, 84)( 68, 83)( 69, 86)( 70, 85)( 71, 88)( 72, 87)
( 73, 94)( 74, 93)( 75, 96)( 76, 95)( 77, 90)( 78, 89)( 79, 92)( 80, 91)
( 97, 98)( 99,100)(101,102)(103,104)(105,110)(106,109)(107,112)(108,111)
(113,130)(114,129)(115,132)(116,131)(117,134)(118,133)(119,136)(120,135)
(121,142)(122,141)(123,144)(124,143)(125,138)(126,137)(127,140)(128,139)
(145,146)(147,148)(149,150)(151,152)(153,158)(154,157)(155,160)(156,159)
(161,178)(162,177)(163,180)(164,179)(165,182)(166,181)(167,184)(168,183)
(169,190)(170,189)(171,192)(172,191)(173,186)(174,185)(175,188)(176,187)
(193,194)(195,196)(197,198)(199,200)(201,206)(202,205)(203,208)(204,207)
(209,226)(210,225)(211,228)(212,227)(213,230)(214,229)(215,232)(216,231)
(217,238)(218,237)(219,240)(220,239)(221,234)(222,233)(223,236)(224,235)
(241,242)(243,244)(245,246)(247,248)(249,254)(250,253)(251,256)(252,255)
(257,274)(258,273)(259,276)(260,275)(261,278)(262,277)(263,280)(264,279)
(265,286)(266,285)(267,288)(268,287)(269,282)(270,281)(271,284)(272,283);;
s3 := ( 1,161)( 2,162)( 3,163)( 4,164)( 5,173)( 6,174)( 7,175)( 8,176)
( 9,169)( 10,170)( 11,171)( 12,172)( 13,165)( 14,166)( 15,167)( 16,168)
( 17,145)( 18,146)( 19,147)( 20,148)( 21,157)( 22,158)( 23,159)( 24,160)
( 25,153)( 26,154)( 27,155)( 28,156)( 29,149)( 30,150)( 31,151)( 32,152)
( 33,177)( 34,178)( 35,179)( 36,180)( 37,189)( 38,190)( 39,191)( 40,192)
( 41,185)( 42,186)( 43,187)( 44,188)( 45,181)( 46,182)( 47,183)( 48,184)
( 49,209)( 50,210)( 51,211)( 52,212)( 53,221)( 54,222)( 55,223)( 56,224)
( 57,217)( 58,218)( 59,219)( 60,220)( 61,213)( 62,214)( 63,215)( 64,216)
( 65,193)( 66,194)( 67,195)( 68,196)( 69,205)( 70,206)( 71,207)( 72,208)
( 73,201)( 74,202)( 75,203)( 76,204)( 77,197)( 78,198)( 79,199)( 80,200)
( 81,225)( 82,226)( 83,227)( 84,228)( 85,237)( 86,238)( 87,239)( 88,240)
( 89,233)( 90,234)( 91,235)( 92,236)( 93,229)( 94,230)( 95,231)( 96,232)
( 97,257)( 98,258)( 99,259)(100,260)(101,269)(102,270)(103,271)(104,272)
(105,265)(106,266)(107,267)(108,268)(109,261)(110,262)(111,263)(112,264)
(113,241)(114,242)(115,243)(116,244)(117,253)(118,254)(119,255)(120,256)
(121,249)(122,250)(123,251)(124,252)(125,245)(126,246)(127,247)(128,248)
(129,273)(130,274)(131,275)(132,276)(133,285)(134,286)(135,287)(136,288)
(137,281)(138,282)(139,283)(140,284)(141,277)(142,278)(143,279)(144,280);;
s4 := ( 1,149)( 2,150)( 3,151)( 4,152)( 5,145)( 6,146)( 7,147)( 8,148)
( 9,153)( 10,154)( 11,155)( 12,156)( 13,157)( 14,158)( 15,159)( 16,160)
( 17,181)( 18,182)( 19,183)( 20,184)( 21,177)( 22,178)( 23,179)( 24,180)
( 25,185)( 26,186)( 27,187)( 28,188)( 29,189)( 30,190)( 31,191)( 32,192)
( 33,165)( 34,166)( 35,167)( 36,168)( 37,161)( 38,162)( 39,163)( 40,164)
( 41,169)( 42,170)( 43,171)( 44,172)( 45,173)( 46,174)( 47,175)( 48,176)
( 49,197)( 50,198)( 51,199)( 52,200)( 53,193)( 54,194)( 55,195)( 56,196)
( 57,201)( 58,202)( 59,203)( 60,204)( 61,205)( 62,206)( 63,207)( 64,208)
( 65,229)( 66,230)( 67,231)( 68,232)( 69,225)( 70,226)( 71,227)( 72,228)
( 73,233)( 74,234)( 75,235)( 76,236)( 77,237)( 78,238)( 79,239)( 80,240)
( 81,213)( 82,214)( 83,215)( 84,216)( 85,209)( 86,210)( 87,211)( 88,212)
( 89,217)( 90,218)( 91,219)( 92,220)( 93,221)( 94,222)( 95,223)( 96,224)
( 97,245)( 98,246)( 99,247)(100,248)(101,241)(102,242)(103,243)(104,244)
(105,249)(106,250)(107,251)(108,252)(109,253)(110,254)(111,255)(112,256)
(113,277)(114,278)(115,279)(116,280)(117,273)(118,274)(119,275)(120,276)
(121,281)(122,282)(123,283)(124,284)(125,285)(126,286)(127,287)(128,288)
(129,261)(130,262)(131,263)(132,264)(133,257)(134,258)(135,259)(136,260)
(137,265)(138,266)(139,267)(140,268)(141,269)(142,270)(143,271)(144,272);;
poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s0*s1*s0*s1*s0*s1,
s3*s4*s3*s4*s3*s4, s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s4*s3*s2*s4*s3*s2*s4*s3*s2*s4*s3,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(288)!( 3, 4)( 7, 8)( 11, 12)( 15, 16)( 19, 20)( 23, 24)( 27, 28)
( 31, 32)( 35, 36)( 39, 40)( 43, 44)( 47, 48)( 49, 97)( 50, 98)( 51,100)
( 52, 99)( 53,101)( 54,102)( 55,104)( 56,103)( 57,105)( 58,106)( 59,108)
( 60,107)( 61,109)( 62,110)( 63,112)( 64,111)( 65,113)( 66,114)( 67,116)
( 68,115)( 69,117)( 70,118)( 71,120)( 72,119)( 73,121)( 74,122)( 75,124)
( 76,123)( 77,125)( 78,126)( 79,128)( 80,127)( 81,129)( 82,130)( 83,132)
( 84,131)( 85,133)( 86,134)( 87,136)( 88,135)( 89,137)( 90,138)( 91,140)
( 92,139)( 93,141)( 94,142)( 95,144)( 96,143)(147,148)(151,152)(155,156)
(159,160)(163,164)(167,168)(171,172)(175,176)(179,180)(183,184)(187,188)
(191,192)(193,241)(194,242)(195,244)(196,243)(197,245)(198,246)(199,248)
(200,247)(201,249)(202,250)(203,252)(204,251)(205,253)(206,254)(207,256)
(208,255)(209,257)(210,258)(211,260)(212,259)(213,261)(214,262)(215,264)
(216,263)(217,265)(218,266)(219,268)(220,267)(221,269)(222,270)(223,272)
(224,271)(225,273)(226,274)(227,276)(228,275)(229,277)(230,278)(231,280)
(232,279)(233,281)(234,282)(235,284)(236,283)(237,285)(238,286)(239,288)
(240,287);
s1 := Sym(288)!( 1, 49)( 2, 52)( 3, 51)( 4, 50)( 5, 53)( 6, 56)( 7, 55)
( 8, 54)( 9, 57)( 10, 60)( 11, 59)( 12, 58)( 13, 61)( 14, 64)( 15, 63)
( 16, 62)( 17, 65)( 18, 68)( 19, 67)( 20, 66)( 21, 69)( 22, 72)( 23, 71)
( 24, 70)( 25, 73)( 26, 76)( 27, 75)( 28, 74)( 29, 77)( 30, 80)( 31, 79)
( 32, 78)( 33, 81)( 34, 84)( 35, 83)( 36, 82)( 37, 85)( 38, 88)( 39, 87)
( 40, 86)( 41, 89)( 42, 92)( 43, 91)( 44, 90)( 45, 93)( 46, 96)( 47, 95)
( 48, 94)( 98,100)(102,104)(106,108)(110,112)(114,116)(118,120)(122,124)
(126,128)(130,132)(134,136)(138,140)(142,144)(145,193)(146,196)(147,195)
(148,194)(149,197)(150,200)(151,199)(152,198)(153,201)(154,204)(155,203)
(156,202)(157,205)(158,208)(159,207)(160,206)(161,209)(162,212)(163,211)
(164,210)(165,213)(166,216)(167,215)(168,214)(169,217)(170,220)(171,219)
(172,218)(173,221)(174,224)(175,223)(176,222)(177,225)(178,228)(179,227)
(180,226)(181,229)(182,232)(183,231)(184,230)(185,233)(186,236)(187,235)
(188,234)(189,237)(190,240)(191,239)(192,238)(242,244)(246,248)(250,252)
(254,256)(258,260)(262,264)(266,268)(270,272)(274,276)(278,280)(282,284)
(286,288);
s2 := Sym(288)!( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9, 14)( 10, 13)( 11, 16)
( 12, 15)( 17, 34)( 18, 33)( 19, 36)( 20, 35)( 21, 38)( 22, 37)( 23, 40)
( 24, 39)( 25, 46)( 26, 45)( 27, 48)( 28, 47)( 29, 42)( 30, 41)( 31, 44)
( 32, 43)( 49, 50)( 51, 52)( 53, 54)( 55, 56)( 57, 62)( 58, 61)( 59, 64)
( 60, 63)( 65, 82)( 66, 81)( 67, 84)( 68, 83)( 69, 86)( 70, 85)( 71, 88)
( 72, 87)( 73, 94)( 74, 93)( 75, 96)( 76, 95)( 77, 90)( 78, 89)( 79, 92)
( 80, 91)( 97, 98)( 99,100)(101,102)(103,104)(105,110)(106,109)(107,112)
(108,111)(113,130)(114,129)(115,132)(116,131)(117,134)(118,133)(119,136)
(120,135)(121,142)(122,141)(123,144)(124,143)(125,138)(126,137)(127,140)
(128,139)(145,146)(147,148)(149,150)(151,152)(153,158)(154,157)(155,160)
(156,159)(161,178)(162,177)(163,180)(164,179)(165,182)(166,181)(167,184)
(168,183)(169,190)(170,189)(171,192)(172,191)(173,186)(174,185)(175,188)
(176,187)(193,194)(195,196)(197,198)(199,200)(201,206)(202,205)(203,208)
(204,207)(209,226)(210,225)(211,228)(212,227)(213,230)(214,229)(215,232)
(216,231)(217,238)(218,237)(219,240)(220,239)(221,234)(222,233)(223,236)
(224,235)(241,242)(243,244)(245,246)(247,248)(249,254)(250,253)(251,256)
(252,255)(257,274)(258,273)(259,276)(260,275)(261,278)(262,277)(263,280)
(264,279)(265,286)(266,285)(267,288)(268,287)(269,282)(270,281)(271,284)
(272,283);
s3 := Sym(288)!( 1,161)( 2,162)( 3,163)( 4,164)( 5,173)( 6,174)( 7,175)
( 8,176)( 9,169)( 10,170)( 11,171)( 12,172)( 13,165)( 14,166)( 15,167)
( 16,168)( 17,145)( 18,146)( 19,147)( 20,148)( 21,157)( 22,158)( 23,159)
( 24,160)( 25,153)( 26,154)( 27,155)( 28,156)( 29,149)( 30,150)( 31,151)
( 32,152)( 33,177)( 34,178)( 35,179)( 36,180)( 37,189)( 38,190)( 39,191)
( 40,192)( 41,185)( 42,186)( 43,187)( 44,188)( 45,181)( 46,182)( 47,183)
( 48,184)( 49,209)( 50,210)( 51,211)( 52,212)( 53,221)( 54,222)( 55,223)
( 56,224)( 57,217)( 58,218)( 59,219)( 60,220)( 61,213)( 62,214)( 63,215)
( 64,216)( 65,193)( 66,194)( 67,195)( 68,196)( 69,205)( 70,206)( 71,207)
( 72,208)( 73,201)( 74,202)( 75,203)( 76,204)( 77,197)( 78,198)( 79,199)
( 80,200)( 81,225)( 82,226)( 83,227)( 84,228)( 85,237)( 86,238)( 87,239)
( 88,240)( 89,233)( 90,234)( 91,235)( 92,236)( 93,229)( 94,230)( 95,231)
( 96,232)( 97,257)( 98,258)( 99,259)(100,260)(101,269)(102,270)(103,271)
(104,272)(105,265)(106,266)(107,267)(108,268)(109,261)(110,262)(111,263)
(112,264)(113,241)(114,242)(115,243)(116,244)(117,253)(118,254)(119,255)
(120,256)(121,249)(122,250)(123,251)(124,252)(125,245)(126,246)(127,247)
(128,248)(129,273)(130,274)(131,275)(132,276)(133,285)(134,286)(135,287)
(136,288)(137,281)(138,282)(139,283)(140,284)(141,277)(142,278)(143,279)
(144,280);
s4 := Sym(288)!( 1,149)( 2,150)( 3,151)( 4,152)( 5,145)( 6,146)( 7,147)
( 8,148)( 9,153)( 10,154)( 11,155)( 12,156)( 13,157)( 14,158)( 15,159)
( 16,160)( 17,181)( 18,182)( 19,183)( 20,184)( 21,177)( 22,178)( 23,179)
( 24,180)( 25,185)( 26,186)( 27,187)( 28,188)( 29,189)( 30,190)( 31,191)
( 32,192)( 33,165)( 34,166)( 35,167)( 36,168)( 37,161)( 38,162)( 39,163)
( 40,164)( 41,169)( 42,170)( 43,171)( 44,172)( 45,173)( 46,174)( 47,175)
( 48,176)( 49,197)( 50,198)( 51,199)( 52,200)( 53,193)( 54,194)( 55,195)
( 56,196)( 57,201)( 58,202)( 59,203)( 60,204)( 61,205)( 62,206)( 63,207)
( 64,208)( 65,229)( 66,230)( 67,231)( 68,232)( 69,225)( 70,226)( 71,227)
( 72,228)( 73,233)( 74,234)( 75,235)( 76,236)( 77,237)( 78,238)( 79,239)
( 80,240)( 81,213)( 82,214)( 83,215)( 84,216)( 85,209)( 86,210)( 87,211)
( 88,212)( 89,217)( 90,218)( 91,219)( 92,220)( 93,221)( 94,222)( 95,223)
( 96,224)( 97,245)( 98,246)( 99,247)(100,248)(101,241)(102,242)(103,243)
(104,244)(105,249)(106,250)(107,251)(108,252)(109,253)(110,254)(111,255)
(112,256)(113,277)(114,278)(115,279)(116,280)(117,273)(118,274)(119,275)
(120,276)(121,281)(122,282)(123,283)(124,284)(125,285)(126,286)(127,287)
(128,288)(129,261)(130,262)(131,263)(132,264)(133,257)(134,258)(135,259)
(136,260)(137,265)(138,266)(139,267)(140,268)(141,269)(142,270)(143,271)
(144,272);
poly := sub<Sym(288)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s0*s2*s0*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4,
s2*s4*s2*s4, s0*s1*s0*s1*s0*s1, s3*s4*s3*s4*s3*s4,
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s4*s3*s2*s4*s3*s2*s4*s3*s2*s4*s3,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;
References : None.
to this polytope