Polytope of Type {2,12,3}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,12,3}*576
if this polytope has a name.
Group : SmallGroup(576,8319)
Rank : 4
Schlafli Type : {2,12,3}
Number of vertices, edges, etc : 2, 48, 72, 12
Order of s0s1s2s3 : 24
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{2,12,3,2} of size 1152
Vertex Figure Of :
{2,2,12,3} of size 1152
{3,2,12,3} of size 1728
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2,6,3}*288
3-fold quotients : {2,12,3}*192
6-fold quotients : {2,6,3}*96
8-fold quotients : {2,6,3}*72
12-fold quotients : {2,3,3}*48
24-fold quotients : {2,2,3}*24
Covers (Minimal Covers in Boldface) :
2-fold covers : {4,12,3}*1152b, {2,12,6}*1152c
3-fold covers : {2,12,9}*1728, {2,12,3}*1728, {6,12,3}*1728
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 3, 75)( 4, 76)( 5, 79)( 6, 80)( 7, 77)( 8, 78)( 9, 82)( 10, 81)
( 11, 83)( 12, 84)( 13, 87)( 14, 88)( 15, 85)( 16, 86)( 17, 90)( 18, 89)
( 19, 91)( 20, 92)( 21, 95)( 22, 96)( 23, 93)( 24, 94)( 25, 98)( 26, 97)
( 27,123)( 28,124)( 29,127)( 30,128)( 31,125)( 32,126)( 33,130)( 34,129)
( 35,131)( 36,132)( 37,135)( 38,136)( 39,133)( 40,134)( 41,138)( 42,137)
( 43,139)( 44,140)( 45,143)( 46,144)( 47,141)( 48,142)( 49,146)( 50,145)
( 51, 99)( 52,100)( 53,103)( 54,104)( 55,101)( 56,102)( 57,106)( 58,105)
( 59,107)( 60,108)( 61,111)( 62,112)( 63,109)( 64,110)( 65,114)( 66,113)
( 67,115)( 68,116)( 69,119)( 70,120)( 71,117)( 72,118)( 73,122)( 74,121)
(147,219)(148,220)(149,223)(150,224)(151,221)(152,222)(153,226)(154,225)
(155,227)(156,228)(157,231)(158,232)(159,229)(160,230)(161,234)(162,233)
(163,235)(164,236)(165,239)(166,240)(167,237)(168,238)(169,242)(170,241)
(171,267)(172,268)(173,271)(174,272)(175,269)(176,270)(177,274)(178,273)
(179,275)(180,276)(181,279)(182,280)(183,277)(184,278)(185,282)(186,281)
(187,283)(188,284)(189,287)(190,288)(191,285)(192,286)(193,290)(194,289)
(195,243)(196,244)(197,247)(198,248)(199,245)(200,246)(201,250)(202,249)
(203,251)(204,252)(205,255)(206,256)(207,253)(208,254)(209,258)(210,257)
(211,259)(212,260)(213,263)(214,264)(215,261)(216,262)(217,266)(218,265);;
s2 := ( 3,243)( 4,244)( 5,246)( 6,245)( 7,249)( 8,250)( 9,247)( 10,248)
( 11,259)( 12,260)( 13,262)( 14,261)( 15,265)( 16,266)( 17,263)( 18,264)
( 19,251)( 20,252)( 21,254)( 22,253)( 23,257)( 24,258)( 25,255)( 26,256)
( 27,219)( 28,220)( 29,222)( 30,221)( 31,225)( 32,226)( 33,223)( 34,224)
( 35,235)( 36,236)( 37,238)( 38,237)( 39,241)( 40,242)( 41,239)( 42,240)
( 43,227)( 44,228)( 45,230)( 46,229)( 47,233)( 48,234)( 49,231)( 50,232)
( 51,267)( 52,268)( 53,270)( 54,269)( 55,273)( 56,274)( 57,271)( 58,272)
( 59,283)( 60,284)( 61,286)( 62,285)( 63,289)( 64,290)( 65,287)( 66,288)
( 67,275)( 68,276)( 69,278)( 70,277)( 71,281)( 72,282)( 73,279)( 74,280)
( 75,172)( 76,171)( 77,173)( 78,174)( 79,178)( 80,177)( 81,176)( 82,175)
( 83,188)( 84,187)( 85,189)( 86,190)( 87,194)( 88,193)( 89,192)( 90,191)
( 91,180)( 92,179)( 93,181)( 94,182)( 95,186)( 96,185)( 97,184)( 98,183)
( 99,148)(100,147)(101,149)(102,150)(103,154)(104,153)(105,152)(106,151)
(107,164)(108,163)(109,165)(110,166)(111,170)(112,169)(113,168)(114,167)
(115,156)(116,155)(117,157)(118,158)(119,162)(120,161)(121,160)(122,159)
(123,196)(124,195)(125,197)(126,198)(127,202)(128,201)(129,200)(130,199)
(131,212)(132,211)(133,213)(134,214)(135,218)(136,217)(137,216)(138,215)
(139,204)(140,203)(141,205)(142,206)(143,210)(144,209)(145,208)(146,207);;
s3 := ( 3,233)( 4,234)( 5,230)( 6,229)( 7,231)( 8,232)( 9,227)( 10,228)
( 11,225)( 12,226)( 13,222)( 14,221)( 15,223)( 16,224)( 17,219)( 18,220)
( 19,241)( 20,242)( 21,238)( 22,237)( 23,239)( 24,240)( 25,235)( 26,236)
( 27,281)( 28,282)( 29,278)( 30,277)( 31,279)( 32,280)( 33,275)( 34,276)
( 35,273)( 36,274)( 37,270)( 38,269)( 39,271)( 40,272)( 41,267)( 42,268)
( 43,289)( 44,290)( 45,286)( 46,285)( 47,287)( 48,288)( 49,283)( 50,284)
( 51,257)( 52,258)( 53,254)( 54,253)( 55,255)( 56,256)( 57,251)( 58,252)
( 59,249)( 60,250)( 61,246)( 62,245)( 63,247)( 64,248)( 65,243)( 66,244)
( 67,265)( 68,266)( 69,262)( 70,261)( 71,263)( 72,264)( 73,259)( 74,260)
( 75,162)( 76,161)( 77,157)( 78,158)( 79,160)( 80,159)( 81,156)( 82,155)
( 83,154)( 84,153)( 85,149)( 86,150)( 87,152)( 88,151)( 89,148)( 90,147)
( 91,170)( 92,169)( 93,165)( 94,166)( 95,168)( 96,167)( 97,164)( 98,163)
( 99,210)(100,209)(101,205)(102,206)(103,208)(104,207)(105,204)(106,203)
(107,202)(108,201)(109,197)(110,198)(111,200)(112,199)(113,196)(114,195)
(115,218)(116,217)(117,213)(118,214)(119,216)(120,215)(121,212)(122,211)
(123,186)(124,185)(125,181)(126,182)(127,184)(128,183)(129,180)(130,179)
(131,178)(132,177)(133,173)(134,174)(135,176)(136,175)(137,172)(138,171)
(139,194)(140,193)(141,189)(142,190)(143,192)(144,191)(145,188)(146,187);;
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*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s2*s3*s2*s3*s2*s3, s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(290)!(1,2);
s1 := Sym(290)!( 3, 75)( 4, 76)( 5, 79)( 6, 80)( 7, 77)( 8, 78)( 9, 82)
( 10, 81)( 11, 83)( 12, 84)( 13, 87)( 14, 88)( 15, 85)( 16, 86)( 17, 90)
( 18, 89)( 19, 91)( 20, 92)( 21, 95)( 22, 96)( 23, 93)( 24, 94)( 25, 98)
( 26, 97)( 27,123)( 28,124)( 29,127)( 30,128)( 31,125)( 32,126)( 33,130)
( 34,129)( 35,131)( 36,132)( 37,135)( 38,136)( 39,133)( 40,134)( 41,138)
( 42,137)( 43,139)( 44,140)( 45,143)( 46,144)( 47,141)( 48,142)( 49,146)
( 50,145)( 51, 99)( 52,100)( 53,103)( 54,104)( 55,101)( 56,102)( 57,106)
( 58,105)( 59,107)( 60,108)( 61,111)( 62,112)( 63,109)( 64,110)( 65,114)
( 66,113)( 67,115)( 68,116)( 69,119)( 70,120)( 71,117)( 72,118)( 73,122)
( 74,121)(147,219)(148,220)(149,223)(150,224)(151,221)(152,222)(153,226)
(154,225)(155,227)(156,228)(157,231)(158,232)(159,229)(160,230)(161,234)
(162,233)(163,235)(164,236)(165,239)(166,240)(167,237)(168,238)(169,242)
(170,241)(171,267)(172,268)(173,271)(174,272)(175,269)(176,270)(177,274)
(178,273)(179,275)(180,276)(181,279)(182,280)(183,277)(184,278)(185,282)
(186,281)(187,283)(188,284)(189,287)(190,288)(191,285)(192,286)(193,290)
(194,289)(195,243)(196,244)(197,247)(198,248)(199,245)(200,246)(201,250)
(202,249)(203,251)(204,252)(205,255)(206,256)(207,253)(208,254)(209,258)
(210,257)(211,259)(212,260)(213,263)(214,264)(215,261)(216,262)(217,266)
(218,265);
s2 := Sym(290)!( 3,243)( 4,244)( 5,246)( 6,245)( 7,249)( 8,250)( 9,247)
( 10,248)( 11,259)( 12,260)( 13,262)( 14,261)( 15,265)( 16,266)( 17,263)
( 18,264)( 19,251)( 20,252)( 21,254)( 22,253)( 23,257)( 24,258)( 25,255)
( 26,256)( 27,219)( 28,220)( 29,222)( 30,221)( 31,225)( 32,226)( 33,223)
( 34,224)( 35,235)( 36,236)( 37,238)( 38,237)( 39,241)( 40,242)( 41,239)
( 42,240)( 43,227)( 44,228)( 45,230)( 46,229)( 47,233)( 48,234)( 49,231)
( 50,232)( 51,267)( 52,268)( 53,270)( 54,269)( 55,273)( 56,274)( 57,271)
( 58,272)( 59,283)( 60,284)( 61,286)( 62,285)( 63,289)( 64,290)( 65,287)
( 66,288)( 67,275)( 68,276)( 69,278)( 70,277)( 71,281)( 72,282)( 73,279)
( 74,280)( 75,172)( 76,171)( 77,173)( 78,174)( 79,178)( 80,177)( 81,176)
( 82,175)( 83,188)( 84,187)( 85,189)( 86,190)( 87,194)( 88,193)( 89,192)
( 90,191)( 91,180)( 92,179)( 93,181)( 94,182)( 95,186)( 96,185)( 97,184)
( 98,183)( 99,148)(100,147)(101,149)(102,150)(103,154)(104,153)(105,152)
(106,151)(107,164)(108,163)(109,165)(110,166)(111,170)(112,169)(113,168)
(114,167)(115,156)(116,155)(117,157)(118,158)(119,162)(120,161)(121,160)
(122,159)(123,196)(124,195)(125,197)(126,198)(127,202)(128,201)(129,200)
(130,199)(131,212)(132,211)(133,213)(134,214)(135,218)(136,217)(137,216)
(138,215)(139,204)(140,203)(141,205)(142,206)(143,210)(144,209)(145,208)
(146,207);
s3 := Sym(290)!( 3,233)( 4,234)( 5,230)( 6,229)( 7,231)( 8,232)( 9,227)
( 10,228)( 11,225)( 12,226)( 13,222)( 14,221)( 15,223)( 16,224)( 17,219)
( 18,220)( 19,241)( 20,242)( 21,238)( 22,237)( 23,239)( 24,240)( 25,235)
( 26,236)( 27,281)( 28,282)( 29,278)( 30,277)( 31,279)( 32,280)( 33,275)
( 34,276)( 35,273)( 36,274)( 37,270)( 38,269)( 39,271)( 40,272)( 41,267)
( 42,268)( 43,289)( 44,290)( 45,286)( 46,285)( 47,287)( 48,288)( 49,283)
( 50,284)( 51,257)( 52,258)( 53,254)( 54,253)( 55,255)( 56,256)( 57,251)
( 58,252)( 59,249)( 60,250)( 61,246)( 62,245)( 63,247)( 64,248)( 65,243)
( 66,244)( 67,265)( 68,266)( 69,262)( 70,261)( 71,263)( 72,264)( 73,259)
( 74,260)( 75,162)( 76,161)( 77,157)( 78,158)( 79,160)( 80,159)( 81,156)
( 82,155)( 83,154)( 84,153)( 85,149)( 86,150)( 87,152)( 88,151)( 89,148)
( 90,147)( 91,170)( 92,169)( 93,165)( 94,166)( 95,168)( 96,167)( 97,164)
( 98,163)( 99,210)(100,209)(101,205)(102,206)(103,208)(104,207)(105,204)
(106,203)(107,202)(108,201)(109,197)(110,198)(111,200)(112,199)(113,196)
(114,195)(115,218)(116,217)(117,213)(118,214)(119,216)(120,215)(121,212)
(122,211)(123,186)(124,185)(125,181)(126,182)(127,184)(128,183)(129,180)
(130,179)(131,178)(132,177)(133,173)(134,174)(135,176)(136,175)(137,172)
(138,171)(139,194)(140,193)(141,189)(142,190)(143,192)(144,191)(145,188)
(146,187);
poly := sub<Sym(290)|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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s2*s3*s2*s3*s2*s3, s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s2 >;
to this polytope