Polytope of Type {4,6,3}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,6,3}*1152c
if this polytope has a name.
Group : SmallGroup(1152,157852)
Rank : 4
Schlafli Type : {4,6,3}
Number of vertices, edges, etc : 32, 96, 72, 3
Order of s0s1s2s3 : 6
Order of s0s1s2s3s2s1 : 4
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 : {4,6,3}*576b
16-fold quotients : {2,6,3}*72
48-fold quotients : {2,2,3}*24
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,153)( 2,154)( 3,155)( 4,156)( 5,157)( 6,158)( 7,159)( 8,160)
( 9,145)( 10,146)( 11,147)( 12,148)( 13,149)( 14,150)( 15,151)( 16,152)
( 17,169)( 18,170)( 19,171)( 20,172)( 21,173)( 22,174)( 23,175)( 24,176)
( 25,161)( 26,162)( 27,163)( 28,164)( 29,165)( 30,166)( 31,167)( 32,168)
( 33,185)( 34,186)( 35,187)( 36,188)( 37,189)( 38,190)( 39,191)( 40,192)
( 41,177)( 42,178)( 43,179)( 44,180)( 45,181)( 46,182)( 47,183)( 48,184)
( 49,201)( 50,202)( 51,203)( 52,204)( 53,205)( 54,206)( 55,207)( 56,208)
( 57,193)( 58,194)( 59,195)( 60,196)( 61,197)( 62,198)( 63,199)( 64,200)
( 65,217)( 66,218)( 67,219)( 68,220)( 69,221)( 70,222)( 71,223)( 72,224)
( 73,209)( 74,210)( 75,211)( 76,212)( 77,213)( 78,214)( 79,215)( 80,216)
( 81,233)( 82,234)( 83,235)( 84,236)( 85,237)( 86,238)( 87,239)( 88,240)
( 89,225)( 90,226)( 91,227)( 92,228)( 93,229)( 94,230)( 95,231)( 96,232)
( 97,249)( 98,250)( 99,251)(100,252)(101,253)(102,254)(103,255)(104,256)
(105,241)(106,242)(107,243)(108,244)(109,245)(110,246)(111,247)(112,248)
(113,265)(114,266)(115,267)(116,268)(117,269)(118,270)(119,271)(120,272)
(121,257)(122,258)(123,259)(124,260)(125,261)(126,262)(127,263)(128,264)
(129,281)(130,282)(131,283)(132,284)(133,285)(134,286)(135,287)(136,288)
(137,273)(138,274)(139,275)(140,276)(141,277)(142,278)(143,279)(144,280);;
s1 := ( 2, 5)( 3, 9)( 4, 13)( 7, 10)( 8, 14)( 12, 15)( 17, 33)( 18, 37)
( 19, 41)( 20, 45)( 21, 34)( 22, 38)( 23, 42)( 24, 46)( 25, 35)( 26, 39)
( 27, 43)( 28, 47)( 29, 36)( 30, 40)( 31, 44)( 32, 48)( 49, 65)( 50, 69)
( 51, 73)( 52, 77)( 53, 66)( 54, 70)( 55, 74)( 56, 78)( 57, 67)( 58, 71)
( 59, 75)( 60, 79)( 61, 68)( 62, 72)( 63, 76)( 64, 80)( 82, 85)( 83, 89)
( 84, 93)( 87, 90)( 88, 94)( 92, 95)( 97,129)( 98,133)( 99,137)(100,141)
(101,130)(102,134)(103,138)(104,142)(105,131)(106,135)(107,139)(108,143)
(109,132)(110,136)(111,140)(112,144)(114,117)(115,121)(116,125)(119,122)
(120,126)(124,127)(146,149)(147,153)(148,157)(151,154)(152,158)(156,159)
(161,177)(162,181)(163,185)(164,189)(165,178)(166,182)(167,186)(168,190)
(169,179)(170,183)(171,187)(172,191)(173,180)(174,184)(175,188)(176,192)
(193,209)(194,213)(195,217)(196,221)(197,210)(198,214)(199,218)(200,222)
(201,211)(202,215)(203,219)(204,223)(205,212)(206,216)(207,220)(208,224)
(226,229)(227,233)(228,237)(231,234)(232,238)(236,239)(241,273)(242,277)
(243,281)(244,285)(245,274)(246,278)(247,282)(248,286)(249,275)(250,279)
(251,283)(252,287)(253,276)(254,280)(255,284)(256,288)(258,261)(259,265)
(260,269)(263,266)(264,270)(268,271);;
s2 := ( 1, 49)( 2, 50)( 3, 52)( 4, 51)( 5, 61)( 6, 62)( 7, 64)( 8, 63)
( 9, 57)( 10, 58)( 11, 60)( 12, 59)( 13, 53)( 14, 54)( 15, 56)( 16, 55)
( 17, 81)( 18, 82)( 19, 84)( 20, 83)( 21, 93)( 22, 94)( 23, 96)( 24, 95)
( 25, 89)( 26, 90)( 27, 92)( 28, 91)( 29, 85)( 30, 86)( 31, 88)( 32, 87)
( 33, 65)( 34, 66)( 35, 68)( 36, 67)( 37, 77)( 38, 78)( 39, 80)( 40, 79)
( 41, 73)( 42, 74)( 43, 76)( 44, 75)( 45, 69)( 46, 70)( 47, 72)( 48, 71)
( 99,100)(101,109)(102,110)(103,112)(104,111)(107,108)(113,129)(114,130)
(115,132)(116,131)(117,141)(118,142)(119,144)(120,143)(121,137)(122,138)
(123,140)(124,139)(125,133)(126,134)(127,136)(128,135)(145,193)(146,194)
(147,196)(148,195)(149,205)(150,206)(151,208)(152,207)(153,201)(154,202)
(155,204)(156,203)(157,197)(158,198)(159,200)(160,199)(161,225)(162,226)
(163,228)(164,227)(165,237)(166,238)(167,240)(168,239)(169,233)(170,234)
(171,236)(172,235)(173,229)(174,230)(175,232)(176,231)(177,209)(178,210)
(179,212)(180,211)(181,221)(182,222)(183,224)(184,223)(185,217)(186,218)
(187,220)(188,219)(189,213)(190,214)(191,216)(192,215)(243,244)(245,253)
(246,254)(247,256)(248,255)(251,252)(257,273)(258,274)(259,276)(260,275)
(261,285)(262,286)(263,288)(264,287)(265,281)(266,282)(267,284)(268,283)
(269,277)(270,278)(271,280)(272,279);;
s3 := ( 1,113)( 2,116)( 3,115)( 4,114)( 5,125)( 6,128)( 7,127)( 8,126)
( 9,121)( 10,124)( 11,123)( 12,122)( 13,117)( 14,120)( 15,119)( 16,118)
( 17, 97)( 18,100)( 19, 99)( 20, 98)( 21,109)( 22,112)( 23,111)( 24,110)
( 25,105)( 26,108)( 27,107)( 28,106)( 29,101)( 30,104)( 31,103)( 32,102)
( 33,129)( 34,132)( 35,131)( 36,130)( 37,141)( 38,144)( 39,143)( 40,142)
( 41,137)( 42,140)( 43,139)( 44,138)( 45,133)( 46,136)( 47,135)( 48,134)
( 49, 65)( 50, 68)( 51, 67)( 52, 66)( 53, 77)( 54, 80)( 55, 79)( 56, 78)
( 57, 73)( 58, 76)( 59, 75)( 60, 74)( 61, 69)( 62, 72)( 63, 71)( 64, 70)
( 82, 84)( 85, 93)( 86, 96)( 87, 95)( 88, 94)( 90, 92)(145,257)(146,260)
(147,259)(148,258)(149,269)(150,272)(151,271)(152,270)(153,265)(154,268)
(155,267)(156,266)(157,261)(158,264)(159,263)(160,262)(161,241)(162,244)
(163,243)(164,242)(165,253)(166,256)(167,255)(168,254)(169,249)(170,252)
(171,251)(172,250)(173,245)(174,248)(175,247)(176,246)(177,273)(178,276)
(179,275)(180,274)(181,285)(182,288)(183,287)(184,286)(185,281)(186,284)
(187,283)(188,282)(189,277)(190,280)(191,279)(192,278)(193,209)(194,212)
(195,211)(196,210)(197,221)(198,224)(199,223)(200,222)(201,217)(202,220)
(203,219)(204,218)(205,213)(206,216)(207,215)(208,214)(226,228)(229,237)
(230,240)(231,239)(232,238)(234,236);;
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, s2*s3*s2*s3*s2*s3,
s0*s1*s0*s1*s0*s1*s0*s1, s3*s1*s2*s1*s2*s3*s1*s2*s1*s2,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1,
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(288)!( 1,153)( 2,154)( 3,155)( 4,156)( 5,157)( 6,158)( 7,159)
( 8,160)( 9,145)( 10,146)( 11,147)( 12,148)( 13,149)( 14,150)( 15,151)
( 16,152)( 17,169)( 18,170)( 19,171)( 20,172)( 21,173)( 22,174)( 23,175)
( 24,176)( 25,161)( 26,162)( 27,163)( 28,164)( 29,165)( 30,166)( 31,167)
( 32,168)( 33,185)( 34,186)( 35,187)( 36,188)( 37,189)( 38,190)( 39,191)
( 40,192)( 41,177)( 42,178)( 43,179)( 44,180)( 45,181)( 46,182)( 47,183)
( 48,184)( 49,201)( 50,202)( 51,203)( 52,204)( 53,205)( 54,206)( 55,207)
( 56,208)( 57,193)( 58,194)( 59,195)( 60,196)( 61,197)( 62,198)( 63,199)
( 64,200)( 65,217)( 66,218)( 67,219)( 68,220)( 69,221)( 70,222)( 71,223)
( 72,224)( 73,209)( 74,210)( 75,211)( 76,212)( 77,213)( 78,214)( 79,215)
( 80,216)( 81,233)( 82,234)( 83,235)( 84,236)( 85,237)( 86,238)( 87,239)
( 88,240)( 89,225)( 90,226)( 91,227)( 92,228)( 93,229)( 94,230)( 95,231)
( 96,232)( 97,249)( 98,250)( 99,251)(100,252)(101,253)(102,254)(103,255)
(104,256)(105,241)(106,242)(107,243)(108,244)(109,245)(110,246)(111,247)
(112,248)(113,265)(114,266)(115,267)(116,268)(117,269)(118,270)(119,271)
(120,272)(121,257)(122,258)(123,259)(124,260)(125,261)(126,262)(127,263)
(128,264)(129,281)(130,282)(131,283)(132,284)(133,285)(134,286)(135,287)
(136,288)(137,273)(138,274)(139,275)(140,276)(141,277)(142,278)(143,279)
(144,280);
s1 := Sym(288)!( 2, 5)( 3, 9)( 4, 13)( 7, 10)( 8, 14)( 12, 15)( 17, 33)
( 18, 37)( 19, 41)( 20, 45)( 21, 34)( 22, 38)( 23, 42)( 24, 46)( 25, 35)
( 26, 39)( 27, 43)( 28, 47)( 29, 36)( 30, 40)( 31, 44)( 32, 48)( 49, 65)
( 50, 69)( 51, 73)( 52, 77)( 53, 66)( 54, 70)( 55, 74)( 56, 78)( 57, 67)
( 58, 71)( 59, 75)( 60, 79)( 61, 68)( 62, 72)( 63, 76)( 64, 80)( 82, 85)
( 83, 89)( 84, 93)( 87, 90)( 88, 94)( 92, 95)( 97,129)( 98,133)( 99,137)
(100,141)(101,130)(102,134)(103,138)(104,142)(105,131)(106,135)(107,139)
(108,143)(109,132)(110,136)(111,140)(112,144)(114,117)(115,121)(116,125)
(119,122)(120,126)(124,127)(146,149)(147,153)(148,157)(151,154)(152,158)
(156,159)(161,177)(162,181)(163,185)(164,189)(165,178)(166,182)(167,186)
(168,190)(169,179)(170,183)(171,187)(172,191)(173,180)(174,184)(175,188)
(176,192)(193,209)(194,213)(195,217)(196,221)(197,210)(198,214)(199,218)
(200,222)(201,211)(202,215)(203,219)(204,223)(205,212)(206,216)(207,220)
(208,224)(226,229)(227,233)(228,237)(231,234)(232,238)(236,239)(241,273)
(242,277)(243,281)(244,285)(245,274)(246,278)(247,282)(248,286)(249,275)
(250,279)(251,283)(252,287)(253,276)(254,280)(255,284)(256,288)(258,261)
(259,265)(260,269)(263,266)(264,270)(268,271);
s2 := Sym(288)!( 1, 49)( 2, 50)( 3, 52)( 4, 51)( 5, 61)( 6, 62)( 7, 64)
( 8, 63)( 9, 57)( 10, 58)( 11, 60)( 12, 59)( 13, 53)( 14, 54)( 15, 56)
( 16, 55)( 17, 81)( 18, 82)( 19, 84)( 20, 83)( 21, 93)( 22, 94)( 23, 96)
( 24, 95)( 25, 89)( 26, 90)( 27, 92)( 28, 91)( 29, 85)( 30, 86)( 31, 88)
( 32, 87)( 33, 65)( 34, 66)( 35, 68)( 36, 67)( 37, 77)( 38, 78)( 39, 80)
( 40, 79)( 41, 73)( 42, 74)( 43, 76)( 44, 75)( 45, 69)( 46, 70)( 47, 72)
( 48, 71)( 99,100)(101,109)(102,110)(103,112)(104,111)(107,108)(113,129)
(114,130)(115,132)(116,131)(117,141)(118,142)(119,144)(120,143)(121,137)
(122,138)(123,140)(124,139)(125,133)(126,134)(127,136)(128,135)(145,193)
(146,194)(147,196)(148,195)(149,205)(150,206)(151,208)(152,207)(153,201)
(154,202)(155,204)(156,203)(157,197)(158,198)(159,200)(160,199)(161,225)
(162,226)(163,228)(164,227)(165,237)(166,238)(167,240)(168,239)(169,233)
(170,234)(171,236)(172,235)(173,229)(174,230)(175,232)(176,231)(177,209)
(178,210)(179,212)(180,211)(181,221)(182,222)(183,224)(184,223)(185,217)
(186,218)(187,220)(188,219)(189,213)(190,214)(191,216)(192,215)(243,244)
(245,253)(246,254)(247,256)(248,255)(251,252)(257,273)(258,274)(259,276)
(260,275)(261,285)(262,286)(263,288)(264,287)(265,281)(266,282)(267,284)
(268,283)(269,277)(270,278)(271,280)(272,279);
s3 := Sym(288)!( 1,113)( 2,116)( 3,115)( 4,114)( 5,125)( 6,128)( 7,127)
( 8,126)( 9,121)( 10,124)( 11,123)( 12,122)( 13,117)( 14,120)( 15,119)
( 16,118)( 17, 97)( 18,100)( 19, 99)( 20, 98)( 21,109)( 22,112)( 23,111)
( 24,110)( 25,105)( 26,108)( 27,107)( 28,106)( 29,101)( 30,104)( 31,103)
( 32,102)( 33,129)( 34,132)( 35,131)( 36,130)( 37,141)( 38,144)( 39,143)
( 40,142)( 41,137)( 42,140)( 43,139)( 44,138)( 45,133)( 46,136)( 47,135)
( 48,134)( 49, 65)( 50, 68)( 51, 67)( 52, 66)( 53, 77)( 54, 80)( 55, 79)
( 56, 78)( 57, 73)( 58, 76)( 59, 75)( 60, 74)( 61, 69)( 62, 72)( 63, 71)
( 64, 70)( 82, 84)( 85, 93)( 86, 96)( 87, 95)( 88, 94)( 90, 92)(145,257)
(146,260)(147,259)(148,258)(149,269)(150,272)(151,271)(152,270)(153,265)
(154,268)(155,267)(156,266)(157,261)(158,264)(159,263)(160,262)(161,241)
(162,244)(163,243)(164,242)(165,253)(166,256)(167,255)(168,254)(169,249)
(170,252)(171,251)(172,250)(173,245)(174,248)(175,247)(176,246)(177,273)
(178,276)(179,275)(180,274)(181,285)(182,288)(183,287)(184,286)(185,281)
(186,284)(187,283)(188,282)(189,277)(190,280)(191,279)(192,278)(193,209)
(194,212)(195,211)(196,210)(197,221)(198,224)(199,223)(200,222)(201,217)
(202,220)(203,219)(204,218)(205,213)(206,216)(207,215)(208,214)(226,228)
(229,237)(230,240)(231,239)(232,238)(234,236);
poly := sub<Sym(288)|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,
s2*s3*s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1,
s3*s1*s2*s1*s2*s3*s1*s2*s1*s2, s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1,
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 >;
References : None.
to this polytope