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Polytope of Type {2,225}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,225}*900
if this polytope has a name.
Group : SmallGroup(900,11)
Rank : 3
Schlafli Type : {2,225}
Number of vertices, edges, etc : 2, 225, 225
Order of s0s1s2 : 450
Order of s0s1s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,225,2} of size 1800
Vertex Figure Of :
   {2,2,225} of size 1800
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {2,75}*300
   5-fold quotients : {2,45}*180
   9-fold quotients : {2,25}*100
   15-fold quotients : {2,15}*60
   25-fold quotients : {2,9}*36
   45-fold quotients : {2,5}*20
   75-fold quotients : {2,3}*12
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,450}*1800
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (  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);;
s2 := (  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);;
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*s1*s0*s1, s0*s2*s0*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*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*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*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*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(227)!(1,2);
s1 := Sym(227)!(  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);
s2 := Sym(227)!(  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);
poly := sub<Sym(227)|s0,s1,s2>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s1*s0*s1, s0*s2*s0*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*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*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*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*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 >; 
 

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