Polytope of Type {20,28}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {20,28}*1120
Also Known As : {20,28|2}. if this polytope has another name.
Group : SmallGroup(1120,530)
Rank : 3
Schlafli Type : {20,28}
Number of vertices, edges, etc : 20, 280, 28
Order of s₀s₁s₂ : 140
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   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 : {20,14}*560, {10,28}*560
   4-fold quotients : {10,14}*280
   5-fold quotients : {4,28}*224
   7-fold quotients : {20,4}*160
   10-fold quotients : {2,28}*112, {4,14}*112
   14-fold quotients : {20,2}*80, {10,4}*80
   20-fold quotients : {2,14}*56
   28-fold quotients : {10,2}*40
   35-fold quotients : {4,4}*32
   40-fold quotients : {2,7}*28
   56-fold quotients : {5,2}*20
   70-fold quotients : {2,4}*16, {4,2}*16
   140-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  8, 29)(  9, 30)( 10, 31)( 11, 32)( 12, 33)( 13, 34)( 14, 35)( 15, 22)
( 16, 23)( 17, 24)( 18, 25)( 19, 26)( 20, 27)( 21, 28)( 43, 64)( 44, 65)
( 45, 66)( 46, 67)( 47, 68)( 48, 69)( 49, 70)( 50, 57)( 51, 58)( 52, 59)
( 53, 60)( 54, 61)( 55, 62)( 56, 63)( 78, 99)( 79,100)( 80,101)( 81,102)
( 82,103)( 83,104)( 84,105)( 85, 92)( 86, 93)( 87, 94)( 88, 95)( 89, 96)
( 90, 97)( 91, 98)(113,134)(114,135)(115,136)(116,137)(117,138)(118,139)
(119,140)(120,127)(121,128)(122,129)(123,130)(124,131)(125,132)(126,133)
(141,211)(142,212)(143,213)(144,214)(145,215)(146,216)(147,217)(148,239)
(149,240)(150,241)(151,242)(152,243)(153,244)(154,245)(155,232)(156,233)
(157,234)(158,235)(159,236)(160,237)(161,238)(162,225)(163,226)(164,227)
(165,228)(166,229)(167,230)(168,231)(169,218)(170,219)(171,220)(172,221)
(173,222)(174,223)(175,224)(176,246)(177,247)(178,248)(179,249)(180,250)
(181,251)(182,252)(183,274)(184,275)(185,276)(186,277)(187,278)(188,279)
(189,280)(190,267)(191,268)(192,269)(193,270)(194,271)(195,272)(196,273)
(197,260)(198,261)(199,262)(200,263)(201,264)(202,265)(203,266)(204,253)
(205,254)(206,255)(207,256)(208,257)(209,258)(210,259);;
s1 := (  1,148)(  2,154)(  3,153)(  4,152)(  5,151)(  6,150)(  7,149)(  8,141)
(  9,147)( 10,146)( 11,145)( 12,144)( 13,143)( 14,142)( 15,169)( 16,175)
( 17,174)( 18,173)( 19,172)( 20,171)( 21,170)( 22,162)( 23,168)( 24,167)
( 25,166)( 26,165)( 27,164)( 28,163)( 29,155)( 30,161)( 31,160)( 32,159)
( 33,158)( 34,157)( 35,156)( 36,183)( 37,189)( 38,188)( 39,187)( 40,186)
( 41,185)( 42,184)( 43,176)( 44,182)( 45,181)( 46,180)( 47,179)( 48,178)
( 49,177)( 50,204)( 51,210)( 52,209)( 53,208)( 54,207)( 55,206)( 56,205)
( 57,197)( 58,203)( 59,202)( 60,201)( 61,200)( 62,199)( 63,198)( 64,190)
( 65,196)( 66,195)( 67,194)( 68,193)( 69,192)( 70,191)( 71,218)( 72,224)
( 73,223)( 74,222)( 75,221)( 76,220)( 77,219)( 78,211)( 79,217)( 80,216)
( 81,215)( 82,214)( 83,213)( 84,212)( 85,239)( 86,245)( 87,244)( 88,243)
( 89,242)( 90,241)( 91,240)( 92,232)( 93,238)( 94,237)( 95,236)( 96,235)
( 97,234)( 98,233)( 99,225)(100,231)(101,230)(102,229)(103,228)(104,227)
(105,226)(106,253)(107,259)(108,258)(109,257)(110,256)(111,255)(112,254)
(113,246)(114,252)(115,251)(116,250)(117,249)(118,248)(119,247)(120,274)
(121,280)(122,279)(123,278)(124,277)(125,276)(126,275)(127,267)(128,273)
(129,272)(130,271)(131,270)(132,269)(133,268)(134,260)(135,266)(136,265)
(137,264)(138,263)(139,262)(140,261);;
s2 := (  1,  2)(  3,  7)(  4,  6)(  8,  9)( 10, 14)( 11, 13)( 15, 16)( 17, 21)
( 18, 20)( 22, 23)( 24, 28)( 25, 27)( 29, 30)( 31, 35)( 32, 34)( 36, 37)
( 38, 42)( 39, 41)( 43, 44)( 45, 49)( 46, 48)( 50, 51)( 52, 56)( 53, 55)
( 57, 58)( 59, 63)( 60, 62)( 64, 65)( 66, 70)( 67, 69)( 71, 72)( 73, 77)
( 74, 76)( 78, 79)( 80, 84)( 81, 83)( 85, 86)( 87, 91)( 88, 90)( 92, 93)
( 94, 98)( 95, 97)( 99,100)(101,105)(102,104)(106,107)(108,112)(109,111)
(113,114)(115,119)(116,118)(120,121)(122,126)(123,125)(127,128)(129,133)
(130,132)(134,135)(136,140)(137,139)(141,177)(142,176)(143,182)(144,181)
(145,180)(146,179)(147,178)(148,184)(149,183)(150,189)(151,188)(152,187)
(153,186)(154,185)(155,191)(156,190)(157,196)(158,195)(159,194)(160,193)
(161,192)(162,198)(163,197)(164,203)(165,202)(166,201)(167,200)(168,199)
(169,205)(170,204)(171,210)(172,209)(173,208)(174,207)(175,206)(211,247)
(212,246)(213,252)(214,251)(215,250)(216,249)(217,248)(218,254)(219,253)
(220,259)(221,258)(222,257)(223,256)(224,255)(225,261)(226,260)(227,266)
(228,265)(229,264)(230,263)(231,262)(232,268)(233,267)(234,273)(235,272)
(236,271)(237,270)(238,269)(239,275)(240,274)(241,280)(242,279)(243,278)
(244,277)(245,276);;
poly := Group([s0,s1,s2]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
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(280)!(  8, 29)(  9, 30)( 10, 31)( 11, 32)( 12, 33)( 13, 34)( 14, 35)
( 15, 22)( 16, 23)( 17, 24)( 18, 25)( 19, 26)( 20, 27)( 21, 28)( 43, 64)
( 44, 65)( 45, 66)( 46, 67)( 47, 68)( 48, 69)( 49, 70)( 50, 57)( 51, 58)
( 52, 59)( 53, 60)( 54, 61)( 55, 62)( 56, 63)( 78, 99)( 79,100)( 80,101)
( 81,102)( 82,103)( 83,104)( 84,105)( 85, 92)( 86, 93)( 87, 94)( 88, 95)
( 89, 96)( 90, 97)( 91, 98)(113,134)(114,135)(115,136)(116,137)(117,138)
(118,139)(119,140)(120,127)(121,128)(122,129)(123,130)(124,131)(125,132)
(126,133)(141,211)(142,212)(143,213)(144,214)(145,215)(146,216)(147,217)
(148,239)(149,240)(150,241)(151,242)(152,243)(153,244)(154,245)(155,232)
(156,233)(157,234)(158,235)(159,236)(160,237)(161,238)(162,225)(163,226)
(164,227)(165,228)(166,229)(167,230)(168,231)(169,218)(170,219)(171,220)
(172,221)(173,222)(174,223)(175,224)(176,246)(177,247)(178,248)(179,249)
(180,250)(181,251)(182,252)(183,274)(184,275)(185,276)(186,277)(187,278)
(188,279)(189,280)(190,267)(191,268)(192,269)(193,270)(194,271)(195,272)
(196,273)(197,260)(198,261)(199,262)(200,263)(201,264)(202,265)(203,266)
(204,253)(205,254)(206,255)(207,256)(208,257)(209,258)(210,259);
s1 := Sym(280)!(  1,148)(  2,154)(  3,153)(  4,152)(  5,151)(  6,150)(  7,149)
(  8,141)(  9,147)( 10,146)( 11,145)( 12,144)( 13,143)( 14,142)( 15,169)
( 16,175)( 17,174)( 18,173)( 19,172)( 20,171)( 21,170)( 22,162)( 23,168)
( 24,167)( 25,166)( 26,165)( 27,164)( 28,163)( 29,155)( 30,161)( 31,160)
( 32,159)( 33,158)( 34,157)( 35,156)( 36,183)( 37,189)( 38,188)( 39,187)
( 40,186)( 41,185)( 42,184)( 43,176)( 44,182)( 45,181)( 46,180)( 47,179)
( 48,178)( 49,177)( 50,204)( 51,210)( 52,209)( 53,208)( 54,207)( 55,206)
( 56,205)( 57,197)( 58,203)( 59,202)( 60,201)( 61,200)( 62,199)( 63,198)
( 64,190)( 65,196)( 66,195)( 67,194)( 68,193)( 69,192)( 70,191)( 71,218)
( 72,224)( 73,223)( 74,222)( 75,221)( 76,220)( 77,219)( 78,211)( 79,217)
( 80,216)( 81,215)( 82,214)( 83,213)( 84,212)( 85,239)( 86,245)( 87,244)
( 88,243)( 89,242)( 90,241)( 91,240)( 92,232)( 93,238)( 94,237)( 95,236)
( 96,235)( 97,234)( 98,233)( 99,225)(100,231)(101,230)(102,229)(103,228)
(104,227)(105,226)(106,253)(107,259)(108,258)(109,257)(110,256)(111,255)
(112,254)(113,246)(114,252)(115,251)(116,250)(117,249)(118,248)(119,247)
(120,274)(121,280)(122,279)(123,278)(124,277)(125,276)(126,275)(127,267)
(128,273)(129,272)(130,271)(131,270)(132,269)(133,268)(134,260)(135,266)
(136,265)(137,264)(138,263)(139,262)(140,261);
s2 := Sym(280)!(  1,  2)(  3,  7)(  4,  6)(  8,  9)( 10, 14)( 11, 13)( 15, 16)
( 17, 21)( 18, 20)( 22, 23)( 24, 28)( 25, 27)( 29, 30)( 31, 35)( 32, 34)
( 36, 37)( 38, 42)( 39, 41)( 43, 44)( 45, 49)( 46, 48)( 50, 51)( 52, 56)
( 53, 55)( 57, 58)( 59, 63)( 60, 62)( 64, 65)( 66, 70)( 67, 69)( 71, 72)
( 73, 77)( 74, 76)( 78, 79)( 80, 84)( 81, 83)( 85, 86)( 87, 91)( 88, 90)
( 92, 93)( 94, 98)( 95, 97)( 99,100)(101,105)(102,104)(106,107)(108,112)
(109,111)(113,114)(115,119)(116,118)(120,121)(122,126)(123,125)(127,128)
(129,133)(130,132)(134,135)(136,140)(137,139)(141,177)(142,176)(143,182)
(144,181)(145,180)(146,179)(147,178)(148,184)(149,183)(150,189)(151,188)
(152,187)(153,186)(154,185)(155,191)(156,190)(157,196)(158,195)(159,194)
(160,193)(161,192)(162,198)(163,197)(164,203)(165,202)(166,201)(167,200)
(168,199)(169,205)(170,204)(171,210)(172,209)(173,208)(174,207)(175,206)
(211,247)(212,246)(213,252)(214,251)(215,250)(216,249)(217,248)(218,254)
(219,253)(220,259)(221,258)(222,257)(223,256)(224,255)(225,261)(226,260)
(227,266)(228,265)(229,264)(230,263)(231,262)(232,268)(233,267)(234,273)
(235,272)(236,271)(237,270)(238,269)(239,275)(240,274)(241,280)(242,279)
(243,278)(244,277)(245,276);
poly := sub<Sym(280)|s0,s1,s2>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
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