Polytope of Type {2,45,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,45,10}*1800
if this polytope has a name.
Group : SmallGroup(1800,317)
Rank : 4
Schlafli Type : {2,45,10}
Number of vertices, edges, etc : 2, 45, 225, 10
Order of s₀s₁s₂s₃ : 90
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 : {2,15,10}*600
   5-fold quotients : {2,45,2}*360
   9-fold quotients : {2,5,10}*200
   15-fold quotients : {2,15,2}*120
   25-fold quotients : {2,9,2}*72
   45-fold quotients : {2,5,2}*40
   75-fold quotients : {2,3,2}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

to this polytope