Polytope of Type {2,18,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,18,10}*1800
if this polytope has a name.
Group : SmallGroup(1800,276)
Rank : 4
Schlafli Type : {2,18,10}
Number of vertices, edges, etc : 2, 45, 225, 25
Order of s₀s₁s₂s₃ : 18
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Non-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 : {2,6,10}*600
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, 89)(  5,100)(  6, 86)(  7, 97)(  8, 98)(  9, 84)( 10, 95)
( 11, 81)( 12, 92)( 13, 93)( 14, 79)( 15, 90)( 16,101)( 17, 87)( 18, 88)
( 19, 99)( 20, 85)( 21, 96)( 22, 82)( 23, 83)( 24, 94)( 25, 80)( 26, 91)
( 27,102)( 28,128)( 29,139)( 30,150)( 31,136)( 32,147)( 33,148)( 34,134)
( 35,145)( 36,131)( 37,142)( 38,143)( 39,129)( 40,140)( 41,151)( 42,137)
( 43,138)( 44,149)( 45,135)( 46,146)( 47,132)( 48,133)( 49,144)( 50,130)
( 51,141)( 52,152)( 53,103)( 54,114)( 55,125)( 56,111)( 57,122)( 58,123)
( 59,109)( 60,120)( 61,106)( 62,117)( 63,118)( 64,104)( 65,115)( 66,126)
( 67,112)( 68,113)( 69,124)( 70,110)( 71,121)( 72,107)( 73,108)( 74,119)
( 75,105)( 76,116)( 77,127)(153,178)(154,189)(155,200)(156,186)(157,197)
(158,198)(159,184)(160,195)(161,181)(162,192)(163,193)(164,179)(165,190)
(166,201)(167,187)(168,188)(169,199)(170,185)(171,196)(172,182)(173,183)
(174,194)(175,180)(176,191)(177,202)(204,214)(205,225)(206,211)(207,222)
(208,223)(210,220)(212,217)(213,218)(216,226)(219,224);;
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, 
s3*s1*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*s2*s3*s1*s2, 
s1*s2*s3*s2*s3*s1*s2*s1*s2*s3*s1*s2*s3*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, 
s1*s3*s2*s1*s3*s2*s1*s3*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, 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, 89)(  5,100)(  6, 86)(  7, 97)(  8, 98)(  9, 84)
( 10, 95)( 11, 81)( 12, 92)( 13, 93)( 14, 79)( 15, 90)( 16,101)( 17, 87)
( 18, 88)( 19, 99)( 20, 85)( 21, 96)( 22, 82)( 23, 83)( 24, 94)( 25, 80)
( 26, 91)( 27,102)( 28,128)( 29,139)( 30,150)( 31,136)( 32,147)( 33,148)
( 34,134)( 35,145)( 36,131)( 37,142)( 38,143)( 39,129)( 40,140)( 41,151)
( 42,137)( 43,138)( 44,149)( 45,135)( 46,146)( 47,132)( 48,133)( 49,144)
( 50,130)( 51,141)( 52,152)( 53,103)( 54,114)( 55,125)( 56,111)( 57,122)
( 58,123)( 59,109)( 60,120)( 61,106)( 62,117)( 63,118)( 64,104)( 65,115)
( 66,126)( 67,112)( 68,113)( 69,124)( 70,110)( 71,121)( 72,107)( 73,108)
( 74,119)( 75,105)( 76,116)( 77,127)(153,178)(154,189)(155,200)(156,186)
(157,197)(158,198)(159,184)(160,195)(161,181)(162,192)(163,193)(164,179)
(165,190)(166,201)(167,187)(168,188)(169,199)(170,185)(171,196)(172,182)
(173,183)(174,194)(175,180)(176,191)(177,202)(204,214)(205,225)(206,211)
(207,222)(208,223)(210,220)(212,217)(213,218)(216,226)(219,224);
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, s3*s1*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*s2*s3*s1*s2, 
s1*s2*s3*s2*s3*s1*s2*s1*s2*s3*s1*s2*s3*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, 
s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

to this polytope