Polytope of Type {2,9,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,9,10}*1800
if this polytope has a name.
Group : SmallGroup(1800,276)
Rank : 4
Schlafli Type : {2,9,10}
Number of vertices, edges, etc : 2, 45, 225, 50
Order of s₀s₁s₂s₃ : 18
Order of s₀s₁s₂s₃s₂s₁ : 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) :
   3-fold quotients : {2,3,10}*600
   25-fold quotients : {2,9,2}*72
   75-fold quotients : {2,3,2}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (  4, 13)(  5, 23)(  6,  8)(  7, 18)(  9, 16)( 10, 26)( 12, 21)( 15, 24)
( 17, 19)( 20, 27)( 28, 53)( 29, 63)( 30, 73)( 31, 58)( 32, 68)( 33, 56)
( 34, 66)( 35, 76)( 36, 61)( 37, 71)( 38, 54)( 39, 64)( 40, 74)( 41, 59)
( 42, 69)( 43, 57)( 44, 67)( 45, 77)( 46, 62)( 47, 72)( 48, 55)( 49, 65)
( 50, 75)( 51, 60)( 52, 70)( 78,178)( 79,188)( 80,198)( 81,183)( 82,193)
( 83,181)( 84,191)( 85,201)( 86,186)( 87,196)( 88,179)( 89,189)( 90,199)
( 91,184)( 92,194)( 93,182)( 94,192)( 95,202)( 96,187)( 97,197)( 98,180)
( 99,190)(100,200)(101,185)(102,195)(103,153)(104,163)(105,173)(106,158)
(107,168)(108,156)(109,166)(110,176)(111,161)(112,171)(113,154)(114,164)
(115,174)(116,159)(117,169)(118,157)(119,167)(120,177)(121,162)(122,172)
(123,155)(124,165)(125,175)(126,160)(127,170)(128,203)(129,213)(130,223)
(131,208)(132,218)(133,206)(134,216)(135,226)(136,211)(137,221)(138,204)
(139,214)(140,224)(141,209)(142,219)(143,207)(144,217)(145,227)(146,212)
(147,222)(148,205)(149,215)(150,225)(151,210)(152,220);;
s2 := (  3, 78)(  4, 97)(  5, 86)(  6,100)(  7, 89)(  8, 83)(  9,102)( 10, 91)
( 11, 80)( 12, 94)( 13, 88)( 14, 82)( 15, 96)( 16, 85)( 17, 99)( 18, 93)
( 19, 87)( 20,101)( 21, 90)( 22, 79)( 23, 98)( 24, 92)( 25, 81)( 26, 95)
( 27, 84)( 28,128)( 29,147)( 30,136)( 31,150)( 32,139)( 33,133)( 34,152)
( 35,141)( 36,130)( 37,144)( 38,138)( 39,132)( 40,146)( 41,135)( 42,149)
( 43,143)( 44,137)( 45,151)( 46,140)( 47,129)( 48,148)( 49,142)( 50,131)
( 51,145)( 52,134)( 53,103)( 54,122)( 55,111)( 56,125)( 57,114)( 58,108)
( 59,127)( 60,116)( 61,105)( 62,119)( 63,113)( 64,107)( 65,121)( 66,110)
( 67,124)( 68,118)( 69,112)( 70,126)( 71,115)( 72,104)( 73,123)( 74,117)
( 75,106)( 76,120)( 77,109)(153,178)(154,197)(155,186)(156,200)(157,189)
(158,183)(159,202)(160,191)(161,180)(162,194)(163,188)(164,182)(165,196)
(166,185)(167,199)(168,193)(169,187)(170,201)(171,190)(172,179)(173,198)
(174,192)(175,181)(176,195)(177,184)(204,222)(205,211)(206,225)(207,214)
(209,227)(210,216)(212,219)(215,221)(217,224)(220,226);;
s3 := (  3, 14)(  4, 13)(  5, 17)(  6, 16)(  7, 15)(  8,  9)( 10, 12)( 18, 24)
( 19, 23)( 20, 27)( 21, 26)( 22, 25)( 28, 39)( 29, 38)( 30, 42)( 31, 41)
( 32, 40)( 33, 34)( 35, 37)( 43, 49)( 44, 48)( 45, 52)( 46, 51)( 47, 50)
( 53, 64)( 54, 63)( 55, 67)( 56, 66)( 57, 65)( 58, 59)( 60, 62)( 68, 74)
( 69, 73)( 70, 77)( 71, 76)( 72, 75)( 78, 89)( 79, 88)( 80, 92)( 81, 91)
( 82, 90)( 83, 84)( 85, 87)( 93, 99)( 94, 98)( 95,102)( 96,101)( 97,100)
(103,114)(104,113)(105,117)(106,116)(107,115)(108,109)(110,112)(118,124)
(119,123)(120,127)(121,126)(122,125)(128,139)(129,138)(130,142)(131,141)
(132,140)(133,134)(135,137)(143,149)(144,148)(145,152)(146,151)(147,150)
(153,164)(154,163)(155,167)(156,166)(157,165)(158,159)(160,162)(168,174)
(169,173)(170,177)(171,176)(172,175)(178,189)(179,188)(180,192)(181,191)
(182,190)(183,184)(185,187)(193,199)(194,198)(195,202)(196,201)(197,200)
(203,214)(204,213)(205,217)(206,216)(207,215)(208,209)(210,212)(218,224)
(219,223)(220,227)(221,226)(222,225);;
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, 
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2, 
s1*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s1*s3*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(227)!(1,2);
s1 := Sym(227)!(  4, 13)(  5, 23)(  6,  8)(  7, 18)(  9, 16)( 10, 26)( 12, 21)
( 15, 24)( 17, 19)( 20, 27)( 28, 53)( 29, 63)( 30, 73)( 31, 58)( 32, 68)
( 33, 56)( 34, 66)( 35, 76)( 36, 61)( 37, 71)( 38, 54)( 39, 64)( 40, 74)
( 41, 59)( 42, 69)( 43, 57)( 44, 67)( 45, 77)( 46, 62)( 47, 72)( 48, 55)
( 49, 65)( 50, 75)( 51, 60)( 52, 70)( 78,178)( 79,188)( 80,198)( 81,183)
( 82,193)( 83,181)( 84,191)( 85,201)( 86,186)( 87,196)( 88,179)( 89,189)
( 90,199)( 91,184)( 92,194)( 93,182)( 94,192)( 95,202)( 96,187)( 97,197)
( 98,180)( 99,190)(100,200)(101,185)(102,195)(103,153)(104,163)(105,173)
(106,158)(107,168)(108,156)(109,166)(110,176)(111,161)(112,171)(113,154)
(114,164)(115,174)(116,159)(117,169)(118,157)(119,167)(120,177)(121,162)
(122,172)(123,155)(124,165)(125,175)(126,160)(127,170)(128,203)(129,213)
(130,223)(131,208)(132,218)(133,206)(134,216)(135,226)(136,211)(137,221)
(138,204)(139,214)(140,224)(141,209)(142,219)(143,207)(144,217)(145,227)
(146,212)(147,222)(148,205)(149,215)(150,225)(151,210)(152,220);
s2 := Sym(227)!(  3, 78)(  4, 97)(  5, 86)(  6,100)(  7, 89)(  8, 83)(  9,102)
( 10, 91)( 11, 80)( 12, 94)( 13, 88)( 14, 82)( 15, 96)( 16, 85)( 17, 99)
( 18, 93)( 19, 87)( 20,101)( 21, 90)( 22, 79)( 23, 98)( 24, 92)( 25, 81)
( 26, 95)( 27, 84)( 28,128)( 29,147)( 30,136)( 31,150)( 32,139)( 33,133)
( 34,152)( 35,141)( 36,130)( 37,144)( 38,138)( 39,132)( 40,146)( 41,135)
( 42,149)( 43,143)( 44,137)( 45,151)( 46,140)( 47,129)( 48,148)( 49,142)
( 50,131)( 51,145)( 52,134)( 53,103)( 54,122)( 55,111)( 56,125)( 57,114)
( 58,108)( 59,127)( 60,116)( 61,105)( 62,119)( 63,113)( 64,107)( 65,121)
( 66,110)( 67,124)( 68,118)( 69,112)( 70,126)( 71,115)( 72,104)( 73,123)
( 74,117)( 75,106)( 76,120)( 77,109)(153,178)(154,197)(155,186)(156,200)
(157,189)(158,183)(159,202)(160,191)(161,180)(162,194)(163,188)(164,182)
(165,196)(166,185)(167,199)(168,193)(169,187)(170,201)(171,190)(172,179)
(173,198)(174,192)(175,181)(176,195)(177,184)(204,222)(205,211)(206,225)
(207,214)(209,227)(210,216)(212,219)(215,221)(217,224)(220,226);
s3 := Sym(227)!(  3, 14)(  4, 13)(  5, 17)(  6, 16)(  7, 15)(  8,  9)( 10, 12)
( 18, 24)( 19, 23)( 20, 27)( 21, 26)( 22, 25)( 28, 39)( 29, 38)( 30, 42)
( 31, 41)( 32, 40)( 33, 34)( 35, 37)( 43, 49)( 44, 48)( 45, 52)( 46, 51)
( 47, 50)( 53, 64)( 54, 63)( 55, 67)( 56, 66)( 57, 65)( 58, 59)( 60, 62)
( 68, 74)( 69, 73)( 70, 77)( 71, 76)( 72, 75)( 78, 89)( 79, 88)( 80, 92)
( 81, 91)( 82, 90)( 83, 84)( 85, 87)( 93, 99)( 94, 98)( 95,102)( 96,101)
( 97,100)(103,114)(104,113)(105,117)(106,116)(107,115)(108,109)(110,112)
(118,124)(119,123)(120,127)(121,126)(122,125)(128,139)(129,138)(130,142)
(131,141)(132,140)(133,134)(135,137)(143,149)(144,148)(145,152)(146,151)
(147,150)(153,164)(154,163)(155,167)(156,166)(157,165)(158,159)(160,162)
(168,174)(169,173)(170,177)(171,176)(172,175)(178,189)(179,188)(180,192)
(181,191)(182,190)(183,184)(185,187)(193,199)(194,198)(195,202)(196,201)
(197,200)(203,214)(204,213)(205,217)(206,216)(207,215)(208,209)(210,212)
(218,224)(219,223)(220,227)(221,226)(222,225);
poly := sub<Sym(227)|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, s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2, 
s1*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s1*s3*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

to this polytope