Polytope of Type {2,2,3,12}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,3,12}*1152
if this polytope has a name.
Group : SmallGroup(1152,157570)
Rank : 5
Schlafli Type : {2,2,3,12}
Number of vertices, edges, etc : 2, 2, 12, 72, 48
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 : {2,2,3,6}*576
3-fold quotients : {2,2,3,12}*384
6-fold quotients : {2,2,3,6}*192
8-fold quotients : {2,2,3,6}*144
12-fold quotients : {2,2,3,3}*96
24-fold quotients : {2,2,3,2}*48
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (3,4);;
s2 := ( 5,221)( 6,222)( 7,225)( 8,226)( 9,223)( 10,224)( 11,228)( 12,227)
( 13,237)( 14,238)( 15,241)( 16,242)( 17,239)( 18,240)( 19,244)( 20,243)
( 21,229)( 22,230)( 23,233)( 24,234)( 25,231)( 26,232)( 27,236)( 28,235)
( 29,269)( 30,270)( 31,273)( 32,274)( 33,271)( 34,272)( 35,276)( 36,275)
( 37,285)( 38,286)( 39,289)( 40,290)( 41,287)( 42,288)( 43,292)( 44,291)
( 45,277)( 46,278)( 47,281)( 48,282)( 49,279)( 50,280)( 51,284)( 52,283)
( 53,245)( 54,246)( 55,249)( 56,250)( 57,247)( 58,248)( 59,252)( 60,251)
( 61,261)( 62,262)( 63,265)( 64,266)( 65,263)( 66,264)( 67,268)( 68,267)
( 69,253)( 70,254)( 71,257)( 72,258)( 73,255)( 74,256)( 75,260)( 76,259)
( 77,150)( 78,149)( 79,154)( 80,153)( 81,152)( 82,151)( 83,155)( 84,156)
( 85,166)( 86,165)( 87,170)( 88,169)( 89,168)( 90,167)( 91,171)( 92,172)
( 93,158)( 94,157)( 95,162)( 96,161)( 97,160)( 98,159)( 99,163)(100,164)
(101,198)(102,197)(103,202)(104,201)(105,200)(106,199)(107,203)(108,204)
(109,214)(110,213)(111,218)(112,217)(113,216)(114,215)(115,219)(116,220)
(117,206)(118,205)(119,210)(120,209)(121,208)(122,207)(123,211)(124,212)
(125,174)(126,173)(127,178)(128,177)(129,176)(130,175)(131,179)(132,180)
(133,190)(134,189)(135,194)(136,193)(137,192)(138,191)(139,195)(140,196)
(141,182)(142,181)(143,186)(144,185)(145,184)(146,183)(147,187)(148,188);;
s3 := ( 5,253)( 6,254)( 7,256)( 8,255)( 9,259)( 10,260)( 11,257)( 12,258)
( 13,245)( 14,246)( 15,248)( 16,247)( 17,251)( 18,252)( 19,249)( 20,250)
( 21,261)( 22,262)( 23,264)( 24,263)( 25,267)( 26,268)( 27,265)( 28,266)
( 29,229)( 30,230)( 31,232)( 32,231)( 33,235)( 34,236)( 35,233)( 36,234)
( 37,221)( 38,222)( 39,224)( 40,223)( 41,227)( 42,228)( 43,225)( 44,226)
( 45,237)( 46,238)( 47,240)( 48,239)( 49,243)( 50,244)( 51,241)( 52,242)
( 53,277)( 54,278)( 55,280)( 56,279)( 57,283)( 58,284)( 59,281)( 60,282)
( 61,269)( 62,270)( 63,272)( 64,271)( 65,275)( 66,276)( 67,273)( 68,274)
( 69,285)( 70,286)( 71,288)( 72,287)( 73,291)( 74,292)( 75,289)( 76,290)
( 77,182)( 78,181)( 79,183)( 80,184)( 81,188)( 82,187)( 83,186)( 84,185)
( 85,174)( 86,173)( 87,175)( 88,176)( 89,180)( 90,179)( 91,178)( 92,177)
( 93,190)( 94,189)( 95,191)( 96,192)( 97,196)( 98,195)( 99,194)(100,193)
(101,158)(102,157)(103,159)(104,160)(105,164)(106,163)(107,162)(108,161)
(109,150)(110,149)(111,151)(112,152)(113,156)(114,155)(115,154)(116,153)
(117,166)(118,165)(119,167)(120,168)(121,172)(122,171)(123,170)(124,169)
(125,206)(126,205)(127,207)(128,208)(129,212)(130,211)(131,210)(132,209)
(133,198)(134,197)(135,199)(136,200)(137,204)(138,203)(139,202)(140,201)
(141,214)(142,213)(143,215)(144,216)(145,220)(146,219)(147,218)(148,217);;
s4 := ( 5, 83)( 6, 84)( 7, 80)( 8, 79)( 9, 81)( 10, 82)( 11, 77)( 12, 78)
( 13, 91)( 14, 92)( 15, 88)( 16, 87)( 17, 89)( 18, 90)( 19, 85)( 20, 86)
( 21, 99)( 22,100)( 23, 96)( 24, 95)( 25, 97)( 26, 98)( 27, 93)( 28, 94)
( 29,131)( 30,132)( 31,128)( 32,127)( 33,129)( 34,130)( 35,125)( 36,126)
( 37,139)( 38,140)( 39,136)( 40,135)( 41,137)( 42,138)( 43,133)( 44,134)
( 45,147)( 46,148)( 47,144)( 48,143)( 49,145)( 50,146)( 51,141)( 52,142)
( 53,107)( 54,108)( 55,104)( 56,103)( 57,105)( 58,106)( 59,101)( 60,102)
( 61,115)( 62,116)( 63,112)( 64,111)( 65,113)( 66,114)( 67,109)( 68,110)
( 69,123)( 70,124)( 71,120)( 72,119)( 73,121)( 74,122)( 75,117)( 76,118)
(149,227)(150,228)(151,224)(152,223)(153,225)(154,226)(155,221)(156,222)
(157,235)(158,236)(159,232)(160,231)(161,233)(162,234)(163,229)(164,230)
(165,243)(166,244)(167,240)(168,239)(169,241)(170,242)(171,237)(172,238)
(173,275)(174,276)(175,272)(176,271)(177,273)(178,274)(179,269)(180,270)
(181,283)(182,284)(183,280)(184,279)(185,281)(186,282)(187,277)(188,278)
(189,291)(190,292)(191,288)(192,287)(193,289)(194,290)(195,285)(196,286)
(197,251)(198,252)(199,248)(200,247)(201,249)(202,250)(203,245)(204,246)
(205,259)(206,260)(207,256)(208,255)(209,257)(210,258)(211,253)(212,254)
(213,267)(214,268)(215,264)(216,263)(217,265)(218,266)(219,261)(220,262);;
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*s1*s0*s1,
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, s2*s3*s2*s3*s2*s3, s4*s2*s3*s4*s3*s4*s2*s3*s4*s2*s3*s4*s2*s3*s4*s3*s4*s2*s3*s4*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(292)!(1,2);
s1 := Sym(292)!(3,4);
s2 := Sym(292)!( 5,221)( 6,222)( 7,225)( 8,226)( 9,223)( 10,224)( 11,228)
( 12,227)( 13,237)( 14,238)( 15,241)( 16,242)( 17,239)( 18,240)( 19,244)
( 20,243)( 21,229)( 22,230)( 23,233)( 24,234)( 25,231)( 26,232)( 27,236)
( 28,235)( 29,269)( 30,270)( 31,273)( 32,274)( 33,271)( 34,272)( 35,276)
( 36,275)( 37,285)( 38,286)( 39,289)( 40,290)( 41,287)( 42,288)( 43,292)
( 44,291)( 45,277)( 46,278)( 47,281)( 48,282)( 49,279)( 50,280)( 51,284)
( 52,283)( 53,245)( 54,246)( 55,249)( 56,250)( 57,247)( 58,248)( 59,252)
( 60,251)( 61,261)( 62,262)( 63,265)( 64,266)( 65,263)( 66,264)( 67,268)
( 68,267)( 69,253)( 70,254)( 71,257)( 72,258)( 73,255)( 74,256)( 75,260)
( 76,259)( 77,150)( 78,149)( 79,154)( 80,153)( 81,152)( 82,151)( 83,155)
( 84,156)( 85,166)( 86,165)( 87,170)( 88,169)( 89,168)( 90,167)( 91,171)
( 92,172)( 93,158)( 94,157)( 95,162)( 96,161)( 97,160)( 98,159)( 99,163)
(100,164)(101,198)(102,197)(103,202)(104,201)(105,200)(106,199)(107,203)
(108,204)(109,214)(110,213)(111,218)(112,217)(113,216)(114,215)(115,219)
(116,220)(117,206)(118,205)(119,210)(120,209)(121,208)(122,207)(123,211)
(124,212)(125,174)(126,173)(127,178)(128,177)(129,176)(130,175)(131,179)
(132,180)(133,190)(134,189)(135,194)(136,193)(137,192)(138,191)(139,195)
(140,196)(141,182)(142,181)(143,186)(144,185)(145,184)(146,183)(147,187)
(148,188);
s3 := Sym(292)!( 5,253)( 6,254)( 7,256)( 8,255)( 9,259)( 10,260)( 11,257)
( 12,258)( 13,245)( 14,246)( 15,248)( 16,247)( 17,251)( 18,252)( 19,249)
( 20,250)( 21,261)( 22,262)( 23,264)( 24,263)( 25,267)( 26,268)( 27,265)
( 28,266)( 29,229)( 30,230)( 31,232)( 32,231)( 33,235)( 34,236)( 35,233)
( 36,234)( 37,221)( 38,222)( 39,224)( 40,223)( 41,227)( 42,228)( 43,225)
( 44,226)( 45,237)( 46,238)( 47,240)( 48,239)( 49,243)( 50,244)( 51,241)
( 52,242)( 53,277)( 54,278)( 55,280)( 56,279)( 57,283)( 58,284)( 59,281)
( 60,282)( 61,269)( 62,270)( 63,272)( 64,271)( 65,275)( 66,276)( 67,273)
( 68,274)( 69,285)( 70,286)( 71,288)( 72,287)( 73,291)( 74,292)( 75,289)
( 76,290)( 77,182)( 78,181)( 79,183)( 80,184)( 81,188)( 82,187)( 83,186)
( 84,185)( 85,174)( 86,173)( 87,175)( 88,176)( 89,180)( 90,179)( 91,178)
( 92,177)( 93,190)( 94,189)( 95,191)( 96,192)( 97,196)( 98,195)( 99,194)
(100,193)(101,158)(102,157)(103,159)(104,160)(105,164)(106,163)(107,162)
(108,161)(109,150)(110,149)(111,151)(112,152)(113,156)(114,155)(115,154)
(116,153)(117,166)(118,165)(119,167)(120,168)(121,172)(122,171)(123,170)
(124,169)(125,206)(126,205)(127,207)(128,208)(129,212)(130,211)(131,210)
(132,209)(133,198)(134,197)(135,199)(136,200)(137,204)(138,203)(139,202)
(140,201)(141,214)(142,213)(143,215)(144,216)(145,220)(146,219)(147,218)
(148,217);
s4 := Sym(292)!( 5, 83)( 6, 84)( 7, 80)( 8, 79)( 9, 81)( 10, 82)( 11, 77)
( 12, 78)( 13, 91)( 14, 92)( 15, 88)( 16, 87)( 17, 89)( 18, 90)( 19, 85)
( 20, 86)( 21, 99)( 22,100)( 23, 96)( 24, 95)( 25, 97)( 26, 98)( 27, 93)
( 28, 94)( 29,131)( 30,132)( 31,128)( 32,127)( 33,129)( 34,130)( 35,125)
( 36,126)( 37,139)( 38,140)( 39,136)( 40,135)( 41,137)( 42,138)( 43,133)
( 44,134)( 45,147)( 46,148)( 47,144)( 48,143)( 49,145)( 50,146)( 51,141)
( 52,142)( 53,107)( 54,108)( 55,104)( 56,103)( 57,105)( 58,106)( 59,101)
( 60,102)( 61,115)( 62,116)( 63,112)( 64,111)( 65,113)( 66,114)( 67,109)
( 68,110)( 69,123)( 70,124)( 71,120)( 72,119)( 73,121)( 74,122)( 75,117)
( 76,118)(149,227)(150,228)(151,224)(152,223)(153,225)(154,226)(155,221)
(156,222)(157,235)(158,236)(159,232)(160,231)(161,233)(162,234)(163,229)
(164,230)(165,243)(166,244)(167,240)(168,239)(169,241)(170,242)(171,237)
(172,238)(173,275)(174,276)(175,272)(176,271)(177,273)(178,274)(179,269)
(180,270)(181,283)(182,284)(183,280)(184,279)(185,281)(186,282)(187,277)
(188,278)(189,291)(190,292)(191,288)(192,287)(193,289)(194,290)(195,285)
(196,286)(197,251)(198,252)(199,248)(200,247)(201,249)(202,250)(203,245)
(204,246)(205,259)(206,260)(207,256)(208,255)(209,257)(210,258)(211,253)
(212,254)(213,267)(214,268)(215,264)(216,263)(217,265)(218,266)(219,261)
(220,262);
poly := sub<Sym(292)|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*s1*s0*s1, 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,
s2*s3*s2*s3*s2*s3, s4*s2*s3*s4*s3*s4*s2*s3*s4*s2*s3*s4*s2*s3*s4*s3*s4*s2*s3*s4*s2*s3 >;
to this polytope