Polytope of Type {3,2,12,3}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,12,3}*1728
if this polytope has a name.
Group : SmallGroup(1728,46303)
Rank : 5
Schlafli Type : {3,2,12,3}
Number of vertices, edges, etc : 3, 3, 48, 72, 12
Order of s0s1s2s3s4 : 24
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
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 : {3,2,6,3}*864
3-fold quotients : {3,2,12,3}*576
6-fold quotients : {3,2,6,3}*288
8-fold quotients : {3,2,6,3}*216
12-fold quotients : {3,2,3,3}*144
24-fold quotients : {3,2,2,3}*72
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (2,3);;
s1 := (1,2);;
s2 := ( 4, 76)( 5, 77)( 6, 80)( 7, 81)( 8, 78)( 9, 79)( 10, 83)( 11, 82)
( 12, 84)( 13, 85)( 14, 88)( 15, 89)( 16, 86)( 17, 87)( 18, 91)( 19, 90)
( 20, 92)( 21, 93)( 22, 96)( 23, 97)( 24, 94)( 25, 95)( 26, 99)( 27, 98)
( 28,124)( 29,125)( 30,128)( 31,129)( 32,126)( 33,127)( 34,131)( 35,130)
( 36,132)( 37,133)( 38,136)( 39,137)( 40,134)( 41,135)( 42,139)( 43,138)
( 44,140)( 45,141)( 46,144)( 47,145)( 48,142)( 49,143)( 50,147)( 51,146)
( 52,100)( 53,101)( 54,104)( 55,105)( 56,102)( 57,103)( 58,107)( 59,106)
( 60,108)( 61,109)( 62,112)( 63,113)( 64,110)( 65,111)( 66,115)( 67,114)
( 68,116)( 69,117)( 70,120)( 71,121)( 72,118)( 73,119)( 74,123)( 75,122)
(148,220)(149,221)(150,224)(151,225)(152,222)(153,223)(154,227)(155,226)
(156,228)(157,229)(158,232)(159,233)(160,230)(161,231)(162,235)(163,234)
(164,236)(165,237)(166,240)(167,241)(168,238)(169,239)(170,243)(171,242)
(172,268)(173,269)(174,272)(175,273)(176,270)(177,271)(178,275)(179,274)
(180,276)(181,277)(182,280)(183,281)(184,278)(185,279)(186,283)(187,282)
(188,284)(189,285)(190,288)(191,289)(192,286)(193,287)(194,291)(195,290)
(196,244)(197,245)(198,248)(199,249)(200,246)(201,247)(202,251)(203,250)
(204,252)(205,253)(206,256)(207,257)(208,254)(209,255)(210,259)(211,258)
(212,260)(213,261)(214,264)(215,265)(216,262)(217,263)(218,267)(219,266);;
s3 := ( 4,244)( 5,245)( 6,247)( 7,246)( 8,250)( 9,251)( 10,248)( 11,249)
( 12,260)( 13,261)( 14,263)( 15,262)( 16,266)( 17,267)( 18,264)( 19,265)
( 20,252)( 21,253)( 22,255)( 23,254)( 24,258)( 25,259)( 26,256)( 27,257)
( 28,220)( 29,221)( 30,223)( 31,222)( 32,226)( 33,227)( 34,224)( 35,225)
( 36,236)( 37,237)( 38,239)( 39,238)( 40,242)( 41,243)( 42,240)( 43,241)
( 44,228)( 45,229)( 46,231)( 47,230)( 48,234)( 49,235)( 50,232)( 51,233)
( 52,268)( 53,269)( 54,271)( 55,270)( 56,274)( 57,275)( 58,272)( 59,273)
( 60,284)( 61,285)( 62,287)( 63,286)( 64,290)( 65,291)( 66,288)( 67,289)
( 68,276)( 69,277)( 70,279)( 71,278)( 72,282)( 73,283)( 74,280)( 75,281)
( 76,173)( 77,172)( 78,174)( 79,175)( 80,179)( 81,178)( 82,177)( 83,176)
( 84,189)( 85,188)( 86,190)( 87,191)( 88,195)( 89,194)( 90,193)( 91,192)
( 92,181)( 93,180)( 94,182)( 95,183)( 96,187)( 97,186)( 98,185)( 99,184)
(100,149)(101,148)(102,150)(103,151)(104,155)(105,154)(106,153)(107,152)
(108,165)(109,164)(110,166)(111,167)(112,171)(113,170)(114,169)(115,168)
(116,157)(117,156)(118,158)(119,159)(120,163)(121,162)(122,161)(123,160)
(124,197)(125,196)(126,198)(127,199)(128,203)(129,202)(130,201)(131,200)
(132,213)(133,212)(134,214)(135,215)(136,219)(137,218)(138,217)(139,216)
(140,205)(141,204)(142,206)(143,207)(144,211)(145,210)(146,209)(147,208);;
s4 := ( 4,234)( 5,235)( 6,231)( 7,230)( 8,232)( 9,233)( 10,228)( 11,229)
( 12,226)( 13,227)( 14,223)( 15,222)( 16,224)( 17,225)( 18,220)( 19,221)
( 20,242)( 21,243)( 22,239)( 23,238)( 24,240)( 25,241)( 26,236)( 27,237)
( 28,282)( 29,283)( 30,279)( 31,278)( 32,280)( 33,281)( 34,276)( 35,277)
( 36,274)( 37,275)( 38,271)( 39,270)( 40,272)( 41,273)( 42,268)( 43,269)
( 44,290)( 45,291)( 46,287)( 47,286)( 48,288)( 49,289)( 50,284)( 51,285)
( 52,258)( 53,259)( 54,255)( 55,254)( 56,256)( 57,257)( 58,252)( 59,253)
( 60,250)( 61,251)( 62,247)( 63,246)( 64,248)( 65,249)( 66,244)( 67,245)
( 68,266)( 69,267)( 70,263)( 71,262)( 72,264)( 73,265)( 74,260)( 75,261)
( 76,163)( 77,162)( 78,158)( 79,159)( 80,161)( 81,160)( 82,157)( 83,156)
( 84,155)( 85,154)( 86,150)( 87,151)( 88,153)( 89,152)( 90,149)( 91,148)
( 92,171)( 93,170)( 94,166)( 95,167)( 96,169)( 97,168)( 98,165)( 99,164)
(100,211)(101,210)(102,206)(103,207)(104,209)(105,208)(106,205)(107,204)
(108,203)(109,202)(110,198)(111,199)(112,201)(113,200)(114,197)(115,196)
(116,219)(117,218)(118,214)(119,215)(120,217)(121,216)(122,213)(123,212)
(124,187)(125,186)(126,182)(127,183)(128,185)(129,184)(130,181)(131,180)
(132,179)(133,178)(134,174)(135,175)(136,177)(137,176)(138,173)(139,172)
(140,195)(141,194)(142,190)(143,191)(144,193)(145,192)(146,189)(147,188);;
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,
s1*s2*s1*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,
s2*s4*s3*s2*s4*s3*s2*s4*s3*s2*s3*s2*s4*s3*s2*s4*s3*s2*s4*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(291)!(2,3);
s1 := Sym(291)!(1,2);
s2 := Sym(291)!( 4, 76)( 5, 77)( 6, 80)( 7, 81)( 8, 78)( 9, 79)( 10, 83)
( 11, 82)( 12, 84)( 13, 85)( 14, 88)( 15, 89)( 16, 86)( 17, 87)( 18, 91)
( 19, 90)( 20, 92)( 21, 93)( 22, 96)( 23, 97)( 24, 94)( 25, 95)( 26, 99)
( 27, 98)( 28,124)( 29,125)( 30,128)( 31,129)( 32,126)( 33,127)( 34,131)
( 35,130)( 36,132)( 37,133)( 38,136)( 39,137)( 40,134)( 41,135)( 42,139)
( 43,138)( 44,140)( 45,141)( 46,144)( 47,145)( 48,142)( 49,143)( 50,147)
( 51,146)( 52,100)( 53,101)( 54,104)( 55,105)( 56,102)( 57,103)( 58,107)
( 59,106)( 60,108)( 61,109)( 62,112)( 63,113)( 64,110)( 65,111)( 66,115)
( 67,114)( 68,116)( 69,117)( 70,120)( 71,121)( 72,118)( 73,119)( 74,123)
( 75,122)(148,220)(149,221)(150,224)(151,225)(152,222)(153,223)(154,227)
(155,226)(156,228)(157,229)(158,232)(159,233)(160,230)(161,231)(162,235)
(163,234)(164,236)(165,237)(166,240)(167,241)(168,238)(169,239)(170,243)
(171,242)(172,268)(173,269)(174,272)(175,273)(176,270)(177,271)(178,275)
(179,274)(180,276)(181,277)(182,280)(183,281)(184,278)(185,279)(186,283)
(187,282)(188,284)(189,285)(190,288)(191,289)(192,286)(193,287)(194,291)
(195,290)(196,244)(197,245)(198,248)(199,249)(200,246)(201,247)(202,251)
(203,250)(204,252)(205,253)(206,256)(207,257)(208,254)(209,255)(210,259)
(211,258)(212,260)(213,261)(214,264)(215,265)(216,262)(217,263)(218,267)
(219,266);
s3 := Sym(291)!( 4,244)( 5,245)( 6,247)( 7,246)( 8,250)( 9,251)( 10,248)
( 11,249)( 12,260)( 13,261)( 14,263)( 15,262)( 16,266)( 17,267)( 18,264)
( 19,265)( 20,252)( 21,253)( 22,255)( 23,254)( 24,258)( 25,259)( 26,256)
( 27,257)( 28,220)( 29,221)( 30,223)( 31,222)( 32,226)( 33,227)( 34,224)
( 35,225)( 36,236)( 37,237)( 38,239)( 39,238)( 40,242)( 41,243)( 42,240)
( 43,241)( 44,228)( 45,229)( 46,231)( 47,230)( 48,234)( 49,235)( 50,232)
( 51,233)( 52,268)( 53,269)( 54,271)( 55,270)( 56,274)( 57,275)( 58,272)
( 59,273)( 60,284)( 61,285)( 62,287)( 63,286)( 64,290)( 65,291)( 66,288)
( 67,289)( 68,276)( 69,277)( 70,279)( 71,278)( 72,282)( 73,283)( 74,280)
( 75,281)( 76,173)( 77,172)( 78,174)( 79,175)( 80,179)( 81,178)( 82,177)
( 83,176)( 84,189)( 85,188)( 86,190)( 87,191)( 88,195)( 89,194)( 90,193)
( 91,192)( 92,181)( 93,180)( 94,182)( 95,183)( 96,187)( 97,186)( 98,185)
( 99,184)(100,149)(101,148)(102,150)(103,151)(104,155)(105,154)(106,153)
(107,152)(108,165)(109,164)(110,166)(111,167)(112,171)(113,170)(114,169)
(115,168)(116,157)(117,156)(118,158)(119,159)(120,163)(121,162)(122,161)
(123,160)(124,197)(125,196)(126,198)(127,199)(128,203)(129,202)(130,201)
(131,200)(132,213)(133,212)(134,214)(135,215)(136,219)(137,218)(138,217)
(139,216)(140,205)(141,204)(142,206)(143,207)(144,211)(145,210)(146,209)
(147,208);
s4 := Sym(291)!( 4,234)( 5,235)( 6,231)( 7,230)( 8,232)( 9,233)( 10,228)
( 11,229)( 12,226)( 13,227)( 14,223)( 15,222)( 16,224)( 17,225)( 18,220)
( 19,221)( 20,242)( 21,243)( 22,239)( 23,238)( 24,240)( 25,241)( 26,236)
( 27,237)( 28,282)( 29,283)( 30,279)( 31,278)( 32,280)( 33,281)( 34,276)
( 35,277)( 36,274)( 37,275)( 38,271)( 39,270)( 40,272)( 41,273)( 42,268)
( 43,269)( 44,290)( 45,291)( 46,287)( 47,286)( 48,288)( 49,289)( 50,284)
( 51,285)( 52,258)( 53,259)( 54,255)( 55,254)( 56,256)( 57,257)( 58,252)
( 59,253)( 60,250)( 61,251)( 62,247)( 63,246)( 64,248)( 65,249)( 66,244)
( 67,245)( 68,266)( 69,267)( 70,263)( 71,262)( 72,264)( 73,265)( 74,260)
( 75,261)( 76,163)( 77,162)( 78,158)( 79,159)( 80,161)( 81,160)( 82,157)
( 83,156)( 84,155)( 85,154)( 86,150)( 87,151)( 88,153)( 89,152)( 90,149)
( 91,148)( 92,171)( 93,170)( 94,166)( 95,167)( 96,169)( 97,168)( 98,165)
( 99,164)(100,211)(101,210)(102,206)(103,207)(104,209)(105,208)(106,205)
(107,204)(108,203)(109,202)(110,198)(111,199)(112,201)(113,200)(114,197)
(115,196)(116,219)(117,218)(118,214)(119,215)(120,217)(121,216)(122,213)
(123,212)(124,187)(125,186)(126,182)(127,183)(128,185)(129,184)(130,181)
(131,180)(132,179)(133,178)(134,174)(135,175)(136,177)(137,176)(138,173)
(139,172)(140,195)(141,194)(142,190)(143,191)(144,193)(145,192)(146,189)
(147,188);
poly := sub<Sym(291)|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, s1*s2*s1*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, s2*s4*s3*s2*s4*s3*s2*s4*s3*s2*s3*s2*s4*s3*s2*s4*s3*s2*s4*s3*s2*s3 >;
to this polytope