Polytope of Type {4,51,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,51,4}*1632
if this polytope has a name.
Group : SmallGroup(1632,1202)
Rank : 4
Schlafli Type : {4,51,4}
Number of vertices, edges, etc : 4, 102, 102, 4
Order of s0s1s2s3 : 51
Order of s0s1s2s3s2s1 : 2
Special Properties :
Universal
Non-Orientable
Flat
Self-Dual
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
17-fold quotients : {4,3,4}*96
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1, 9)( 2, 10)( 3, 11)( 4, 12)( 5, 13)( 6, 14)( 7, 15)( 8, 16)
( 17, 25)( 18, 26)( 19, 27)( 20, 28)( 21, 29)( 22, 30)( 23, 31)( 24, 32)
( 33, 41)( 34, 42)( 35, 43)( 36, 44)( 37, 45)( 38, 46)( 39, 47)( 40, 48)
( 49, 57)( 50, 58)( 51, 59)( 52, 60)( 53, 61)( 54, 62)( 55, 63)( 56, 64)
( 65, 73)( 66, 74)( 67, 75)( 68, 76)( 69, 77)( 70, 78)( 71, 79)( 72, 80)
( 81, 89)( 82, 90)( 83, 91)( 84, 92)( 85, 93)( 86, 94)( 87, 95)( 88, 96)
( 97,105)( 98,106)( 99,107)(100,108)(101,109)(102,110)(103,111)(104,112)
(113,121)(114,122)(115,123)(116,124)(117,125)(118,126)(119,127)(120,128)
(129,137)(130,138)(131,139)(132,140)(133,141)(134,142)(135,143)(136,144)
(145,153)(146,154)(147,155)(148,156)(149,157)(150,158)(151,159)(152,160)
(161,169)(162,170)(163,171)(164,172)(165,173)(166,174)(167,175)(168,176)
(177,185)(178,186)(179,187)(180,188)(181,189)(182,190)(183,191)(184,192)
(193,201)(194,202)(195,203)(196,204)(197,205)(198,206)(199,207)(200,208)
(209,217)(210,218)(211,219)(212,220)(213,221)(214,222)(215,223)(216,224)
(225,233)(226,234)(227,235)(228,236)(229,237)(230,238)(231,239)(232,240)
(241,249)(242,250)(243,251)(244,252)(245,253)(246,254)(247,255)(248,256)
(257,265)(258,266)(259,267)(260,268)(261,269)(262,270)(263,271)(264,272);;
s1 := ( 3, 4)( 7, 8)( 9, 13)( 10, 14)( 11, 16)( 12, 15)( 17,257)( 18,258)
( 19,260)( 20,259)( 21,261)( 22,262)( 23,264)( 24,263)( 25,269)( 26,270)
( 27,272)( 28,271)( 29,265)( 30,266)( 31,268)( 32,267)( 33,241)( 34,242)
( 35,244)( 36,243)( 37,245)( 38,246)( 39,248)( 40,247)( 41,253)( 42,254)
( 43,256)( 44,255)( 45,249)( 46,250)( 47,252)( 48,251)( 49,225)( 50,226)
( 51,228)( 52,227)( 53,229)( 54,230)( 55,232)( 56,231)( 57,237)( 58,238)
( 59,240)( 60,239)( 61,233)( 62,234)( 63,236)( 64,235)( 65,209)( 66,210)
( 67,212)( 68,211)( 69,213)( 70,214)( 71,216)( 72,215)( 73,221)( 74,222)
( 75,224)( 76,223)( 77,217)( 78,218)( 79,220)( 80,219)( 81,193)( 82,194)
( 83,196)( 84,195)( 85,197)( 86,198)( 87,200)( 88,199)( 89,205)( 90,206)
( 91,208)( 92,207)( 93,201)( 94,202)( 95,204)( 96,203)( 97,177)( 98,178)
( 99,180)(100,179)(101,181)(102,182)(103,184)(104,183)(105,189)(106,190)
(107,192)(108,191)(109,185)(110,186)(111,188)(112,187)(113,161)(114,162)
(115,164)(116,163)(117,165)(118,166)(119,168)(120,167)(121,173)(122,174)
(123,176)(124,175)(125,169)(126,170)(127,172)(128,171)(129,145)(130,146)
(131,148)(132,147)(133,149)(134,150)(135,152)(136,151)(137,157)(138,158)
(139,160)(140,159)(141,153)(142,154)(143,156)(144,155);;
s2 := ( 1, 17)( 2, 20)( 3, 19)( 4, 18)( 5, 29)( 6, 32)( 7, 31)( 8, 30)
( 9, 25)( 10, 28)( 11, 27)( 12, 26)( 13, 21)( 14, 24)( 15, 23)( 16, 22)
( 33,257)( 34,260)( 35,259)( 36,258)( 37,269)( 38,272)( 39,271)( 40,270)
( 41,265)( 42,268)( 43,267)( 44,266)( 45,261)( 46,264)( 47,263)( 48,262)
( 49,241)( 50,244)( 51,243)( 52,242)( 53,253)( 54,256)( 55,255)( 56,254)
( 57,249)( 58,252)( 59,251)( 60,250)( 61,245)( 62,248)( 63,247)( 64,246)
( 65,225)( 66,228)( 67,227)( 68,226)( 69,237)( 70,240)( 71,239)( 72,238)
( 73,233)( 74,236)( 75,235)( 76,234)( 77,229)( 78,232)( 79,231)( 80,230)
( 81,209)( 82,212)( 83,211)( 84,210)( 85,221)( 86,224)( 87,223)( 88,222)
( 89,217)( 90,220)( 91,219)( 92,218)( 93,213)( 94,216)( 95,215)( 96,214)
( 97,193)( 98,196)( 99,195)(100,194)(101,205)(102,208)(103,207)(104,206)
(105,201)(106,204)(107,203)(108,202)(109,197)(110,200)(111,199)(112,198)
(113,177)(114,180)(115,179)(116,178)(117,189)(118,192)(119,191)(120,190)
(121,185)(122,188)(123,187)(124,186)(125,181)(126,184)(127,183)(128,182)
(129,161)(130,164)(131,163)(132,162)(133,173)(134,176)(135,175)(136,174)
(137,169)(138,172)(139,171)(140,170)(141,165)(142,168)(143,167)(144,166)
(146,148)(149,157)(150,160)(151,159)(152,158)(154,156);;
s3 := ( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9, 10)( 11, 12)( 13, 14)( 15, 16)
( 17, 18)( 19, 20)( 21, 22)( 23, 24)( 25, 26)( 27, 28)( 29, 30)( 31, 32)
( 33, 34)( 35, 36)( 37, 38)( 39, 40)( 41, 42)( 43, 44)( 45, 46)( 47, 48)
( 49, 50)( 51, 52)( 53, 54)( 55, 56)( 57, 58)( 59, 60)( 61, 62)( 63, 64)
( 65, 66)( 67, 68)( 69, 70)( 71, 72)( 73, 74)( 75, 76)( 77, 78)( 79, 80)
( 81, 82)( 83, 84)( 85, 86)( 87, 88)( 89, 90)( 91, 92)( 93, 94)( 95, 96)
( 97, 98)( 99,100)(101,102)(103,104)(105,106)(107,108)(109,110)(111,112)
(113,114)(115,116)(117,118)(119,120)(121,122)(123,124)(125,126)(127,128)
(129,130)(131,132)(133,134)(135,136)(137,138)(139,140)(141,142)(143,144)
(145,146)(147,148)(149,150)(151,152)(153,154)(155,156)(157,158)(159,160)
(161,162)(163,164)(165,166)(167,168)(169,170)(171,172)(173,174)(175,176)
(177,178)(179,180)(181,182)(183,184)(185,186)(187,188)(189,190)(191,192)
(193,194)(195,196)(197,198)(199,200)(201,202)(203,204)(205,206)(207,208)
(209,210)(211,212)(213,214)(215,216)(217,218)(219,220)(221,222)(223,224)
(225,226)(227,228)(229,230)(231,232)(233,234)(235,236)(237,238)(239,240)
(241,242)(243,244)(245,246)(247,248)(249,250)(251,252)(253,254)(255,256)
(257,258)(259,260)(261,262)(263,264)(265,266)(267,268)(269,270)(271,272);;
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, s0*s1*s0*s1*s0*s1*s0*s1,
s2*s3*s2*s3*s2*s3*s2*s3, s0*s1*s2*s1*s0*s1*s2*s0*s1,
s3*s2*s1*s3*s2*s3*s2*s1*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(272)!( 1, 9)( 2, 10)( 3, 11)( 4, 12)( 5, 13)( 6, 14)( 7, 15)
( 8, 16)( 17, 25)( 18, 26)( 19, 27)( 20, 28)( 21, 29)( 22, 30)( 23, 31)
( 24, 32)( 33, 41)( 34, 42)( 35, 43)( 36, 44)( 37, 45)( 38, 46)( 39, 47)
( 40, 48)( 49, 57)( 50, 58)( 51, 59)( 52, 60)( 53, 61)( 54, 62)( 55, 63)
( 56, 64)( 65, 73)( 66, 74)( 67, 75)( 68, 76)( 69, 77)( 70, 78)( 71, 79)
( 72, 80)( 81, 89)( 82, 90)( 83, 91)( 84, 92)( 85, 93)( 86, 94)( 87, 95)
( 88, 96)( 97,105)( 98,106)( 99,107)(100,108)(101,109)(102,110)(103,111)
(104,112)(113,121)(114,122)(115,123)(116,124)(117,125)(118,126)(119,127)
(120,128)(129,137)(130,138)(131,139)(132,140)(133,141)(134,142)(135,143)
(136,144)(145,153)(146,154)(147,155)(148,156)(149,157)(150,158)(151,159)
(152,160)(161,169)(162,170)(163,171)(164,172)(165,173)(166,174)(167,175)
(168,176)(177,185)(178,186)(179,187)(180,188)(181,189)(182,190)(183,191)
(184,192)(193,201)(194,202)(195,203)(196,204)(197,205)(198,206)(199,207)
(200,208)(209,217)(210,218)(211,219)(212,220)(213,221)(214,222)(215,223)
(216,224)(225,233)(226,234)(227,235)(228,236)(229,237)(230,238)(231,239)
(232,240)(241,249)(242,250)(243,251)(244,252)(245,253)(246,254)(247,255)
(248,256)(257,265)(258,266)(259,267)(260,268)(261,269)(262,270)(263,271)
(264,272);
s1 := Sym(272)!( 3, 4)( 7, 8)( 9, 13)( 10, 14)( 11, 16)( 12, 15)( 17,257)
( 18,258)( 19,260)( 20,259)( 21,261)( 22,262)( 23,264)( 24,263)( 25,269)
( 26,270)( 27,272)( 28,271)( 29,265)( 30,266)( 31,268)( 32,267)( 33,241)
( 34,242)( 35,244)( 36,243)( 37,245)( 38,246)( 39,248)( 40,247)( 41,253)
( 42,254)( 43,256)( 44,255)( 45,249)( 46,250)( 47,252)( 48,251)( 49,225)
( 50,226)( 51,228)( 52,227)( 53,229)( 54,230)( 55,232)( 56,231)( 57,237)
( 58,238)( 59,240)( 60,239)( 61,233)( 62,234)( 63,236)( 64,235)( 65,209)
( 66,210)( 67,212)( 68,211)( 69,213)( 70,214)( 71,216)( 72,215)( 73,221)
( 74,222)( 75,224)( 76,223)( 77,217)( 78,218)( 79,220)( 80,219)( 81,193)
( 82,194)( 83,196)( 84,195)( 85,197)( 86,198)( 87,200)( 88,199)( 89,205)
( 90,206)( 91,208)( 92,207)( 93,201)( 94,202)( 95,204)( 96,203)( 97,177)
( 98,178)( 99,180)(100,179)(101,181)(102,182)(103,184)(104,183)(105,189)
(106,190)(107,192)(108,191)(109,185)(110,186)(111,188)(112,187)(113,161)
(114,162)(115,164)(116,163)(117,165)(118,166)(119,168)(120,167)(121,173)
(122,174)(123,176)(124,175)(125,169)(126,170)(127,172)(128,171)(129,145)
(130,146)(131,148)(132,147)(133,149)(134,150)(135,152)(136,151)(137,157)
(138,158)(139,160)(140,159)(141,153)(142,154)(143,156)(144,155);
s2 := Sym(272)!( 1, 17)( 2, 20)( 3, 19)( 4, 18)( 5, 29)( 6, 32)( 7, 31)
( 8, 30)( 9, 25)( 10, 28)( 11, 27)( 12, 26)( 13, 21)( 14, 24)( 15, 23)
( 16, 22)( 33,257)( 34,260)( 35,259)( 36,258)( 37,269)( 38,272)( 39,271)
( 40,270)( 41,265)( 42,268)( 43,267)( 44,266)( 45,261)( 46,264)( 47,263)
( 48,262)( 49,241)( 50,244)( 51,243)( 52,242)( 53,253)( 54,256)( 55,255)
( 56,254)( 57,249)( 58,252)( 59,251)( 60,250)( 61,245)( 62,248)( 63,247)
( 64,246)( 65,225)( 66,228)( 67,227)( 68,226)( 69,237)( 70,240)( 71,239)
( 72,238)( 73,233)( 74,236)( 75,235)( 76,234)( 77,229)( 78,232)( 79,231)
( 80,230)( 81,209)( 82,212)( 83,211)( 84,210)( 85,221)( 86,224)( 87,223)
( 88,222)( 89,217)( 90,220)( 91,219)( 92,218)( 93,213)( 94,216)( 95,215)
( 96,214)( 97,193)( 98,196)( 99,195)(100,194)(101,205)(102,208)(103,207)
(104,206)(105,201)(106,204)(107,203)(108,202)(109,197)(110,200)(111,199)
(112,198)(113,177)(114,180)(115,179)(116,178)(117,189)(118,192)(119,191)
(120,190)(121,185)(122,188)(123,187)(124,186)(125,181)(126,184)(127,183)
(128,182)(129,161)(130,164)(131,163)(132,162)(133,173)(134,176)(135,175)
(136,174)(137,169)(138,172)(139,171)(140,170)(141,165)(142,168)(143,167)
(144,166)(146,148)(149,157)(150,160)(151,159)(152,158)(154,156);
s3 := Sym(272)!( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9, 10)( 11, 12)( 13, 14)
( 15, 16)( 17, 18)( 19, 20)( 21, 22)( 23, 24)( 25, 26)( 27, 28)( 29, 30)
( 31, 32)( 33, 34)( 35, 36)( 37, 38)( 39, 40)( 41, 42)( 43, 44)( 45, 46)
( 47, 48)( 49, 50)( 51, 52)( 53, 54)( 55, 56)( 57, 58)( 59, 60)( 61, 62)
( 63, 64)( 65, 66)( 67, 68)( 69, 70)( 71, 72)( 73, 74)( 75, 76)( 77, 78)
( 79, 80)( 81, 82)( 83, 84)( 85, 86)( 87, 88)( 89, 90)( 91, 92)( 93, 94)
( 95, 96)( 97, 98)( 99,100)(101,102)(103,104)(105,106)(107,108)(109,110)
(111,112)(113,114)(115,116)(117,118)(119,120)(121,122)(123,124)(125,126)
(127,128)(129,130)(131,132)(133,134)(135,136)(137,138)(139,140)(141,142)
(143,144)(145,146)(147,148)(149,150)(151,152)(153,154)(155,156)(157,158)
(159,160)(161,162)(163,164)(165,166)(167,168)(169,170)(171,172)(173,174)
(175,176)(177,178)(179,180)(181,182)(183,184)(185,186)(187,188)(189,190)
(191,192)(193,194)(195,196)(197,198)(199,200)(201,202)(203,204)(205,206)
(207,208)(209,210)(211,212)(213,214)(215,216)(217,218)(219,220)(221,222)
(223,224)(225,226)(227,228)(229,230)(231,232)(233,234)(235,236)(237,238)
(239,240)(241,242)(243,244)(245,246)(247,248)(249,250)(251,252)(253,254)
(255,256)(257,258)(259,260)(261,262)(263,264)(265,266)(267,268)(269,270)
(271,272);
poly := sub<Sym(272)|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,
s0*s1*s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3,
s0*s1*s2*s1*s0*s1*s2*s0*s1, s3*s2*s1*s3*s2*s3*s2*s1*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
References : None.
to this polytope