Polytope of Type {2,10,18}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,10,18}*1800
if this polytope has a name.
Group : SmallGroup(1800,276)
Rank : 4
Schlafli Type : {2,10,18}
Number of vertices, edges, etc : 2, 25, 225, 45
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 : {2,10,6}*600
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope