Polytope of Type {2,15,30}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,15,30}*1800
if this polytope has a name.
Group : SmallGroup(1800,736)
Rank : 4
Schlafli Type : {2,15,30}
Number of vertices, edges, etc : 2, 15, 225, 30
Order of s₀s₁s₂s₃ : 30
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 : {2,15,6}*360
   9-fold quotients : {2,5,10}*200
   15-fold quotients : {2,15,2}*120
   25-fold quotients : {2,3,6}*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,  7)(  5,  6)(  8, 23)(  9, 27)( 10, 26)( 11, 25)( 12, 24)( 13, 18)
( 14, 22)( 15, 21)( 16, 20)( 17, 19)( 28, 53)( 29, 57)( 30, 56)( 31, 55)
( 32, 54)( 33, 73)( 34, 77)( 35, 76)( 36, 75)( 37, 74)( 38, 68)( 39, 72)
( 40, 71)( 41, 70)( 42, 69)( 43, 63)( 44, 67)( 45, 66)( 46, 65)( 47, 64)
( 48, 58)( 49, 62)( 50, 61)( 51, 60)( 52, 59)( 78,153)( 79,157)( 80,156)
( 81,155)( 82,154)( 83,173)( 84,177)( 85,176)( 86,175)( 87,174)( 88,168)
( 89,172)( 90,171)( 91,170)( 92,169)( 93,163)( 94,167)( 95,166)( 96,165)
( 97,164)( 98,158)( 99,162)(100,161)(101,160)(102,159)(103,203)(104,207)
(105,206)(106,205)(107,204)(108,223)(109,227)(110,226)(111,225)(112,224)
(113,218)(114,222)(115,221)(116,220)(117,219)(118,213)(119,217)(120,216)
(121,215)(122,214)(123,208)(124,212)(125,211)(126,210)(127,209)(128,178)
(129,182)(130,181)(131,180)(132,179)(133,198)(134,202)(135,201)(136,200)
(137,199)(138,193)(139,197)(140,196)(141,195)(142,194)(143,188)(144,192)
(145,191)(146,190)(147,189)(148,183)(149,187)(150,186)(151,185)(152,184);;
s2 := (  3,109)(  4,108)(  5,112)(  6,111)(  7,110)(  8,104)(  9,103)( 10,107)
( 11,106)( 12,105)( 13,124)( 14,123)( 15,127)( 16,126)( 17,125)( 18,119)
( 19,118)( 20,122)( 21,121)( 22,120)( 23,114)( 24,113)( 25,117)( 26,116)
( 27,115)( 28, 84)( 29, 83)( 30, 87)( 31, 86)( 32, 85)( 33, 79)( 34, 78)
( 35, 82)( 36, 81)( 37, 80)( 38, 99)( 39, 98)( 40,102)( 41,101)( 42,100)
( 43, 94)( 44, 93)( 45, 97)( 46, 96)( 47, 95)( 48, 89)( 49, 88)( 50, 92)
( 51, 91)( 52, 90)( 53,134)( 54,133)( 55,137)( 56,136)( 57,135)( 58,129)
( 59,128)( 60,132)( 61,131)( 62,130)( 63,149)( 64,148)( 65,152)( 66,151)
( 67,150)( 68,144)( 69,143)( 70,147)( 71,146)( 72,145)( 73,139)( 74,138)
( 75,142)( 76,141)( 77,140)(153,184)(154,183)(155,187)(156,186)(157,185)
(158,179)(159,178)(160,182)(161,181)(162,180)(163,199)(164,198)(165,202)
(166,201)(167,200)(168,194)(169,193)(170,197)(171,196)(172,195)(173,189)
(174,188)(175,192)(176,191)(177,190)(203,209)(204,208)(205,212)(206,211)
(207,210)(213,224)(214,223)(215,227)(216,226)(217,225)(218,219)(220,222);;
s3 := (  4,  7)(  5,  6)(  9, 12)( 10, 11)( 14, 17)( 15, 16)( 19, 22)( 20, 21)
( 24, 27)( 25, 26)( 28, 53)( 29, 57)( 30, 56)( 31, 55)( 32, 54)( 33, 58)
( 34, 62)( 35, 61)( 36, 60)( 37, 59)( 38, 63)( 39, 67)( 40, 66)( 41, 65)
( 42, 64)( 43, 68)( 44, 72)( 45, 71)( 46, 70)( 47, 69)( 48, 73)( 49, 77)
( 50, 76)( 51, 75)( 52, 74)( 79, 82)( 80, 81)( 84, 87)( 85, 86)( 89, 92)
( 90, 91)( 94, 97)( 95, 96)( 99,102)(100,101)(103,128)(104,132)(105,131)
(106,130)(107,129)(108,133)(109,137)(110,136)(111,135)(112,134)(113,138)
(114,142)(115,141)(116,140)(117,139)(118,143)(119,147)(120,146)(121,145)
(122,144)(123,148)(124,152)(125,151)(126,150)(127,149)(154,157)(155,156)
(159,162)(160,161)(164,167)(165,166)(169,172)(170,171)(174,177)(175,176)
(178,203)(179,207)(180,206)(181,205)(182,204)(183,208)(184,212)(185,211)
(186,210)(187,209)(188,213)(189,217)(190,216)(191,215)(192,214)(193,218)
(194,222)(195,221)(196,220)(197,219)(198,223)(199,227)(200,226)(201,225)
(202,224);;
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*s1*s2*s1*s2*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,  7)(  5,  6)(  8, 23)(  9, 27)( 10, 26)( 11, 25)( 12, 24)
( 13, 18)( 14, 22)( 15, 21)( 16, 20)( 17, 19)( 28, 53)( 29, 57)( 30, 56)
( 31, 55)( 32, 54)( 33, 73)( 34, 77)( 35, 76)( 36, 75)( 37, 74)( 38, 68)
( 39, 72)( 40, 71)( 41, 70)( 42, 69)( 43, 63)( 44, 67)( 45, 66)( 46, 65)
( 47, 64)( 48, 58)( 49, 62)( 50, 61)( 51, 60)( 52, 59)( 78,153)( 79,157)
( 80,156)( 81,155)( 82,154)( 83,173)( 84,177)( 85,176)( 86,175)( 87,174)
( 88,168)( 89,172)( 90,171)( 91,170)( 92,169)( 93,163)( 94,167)( 95,166)
( 96,165)( 97,164)( 98,158)( 99,162)(100,161)(101,160)(102,159)(103,203)
(104,207)(105,206)(106,205)(107,204)(108,223)(109,227)(110,226)(111,225)
(112,224)(113,218)(114,222)(115,221)(116,220)(117,219)(118,213)(119,217)
(120,216)(121,215)(122,214)(123,208)(124,212)(125,211)(126,210)(127,209)
(128,178)(129,182)(130,181)(131,180)(132,179)(133,198)(134,202)(135,201)
(136,200)(137,199)(138,193)(139,197)(140,196)(141,195)(142,194)(143,188)
(144,192)(145,191)(146,190)(147,189)(148,183)(149,187)(150,186)(151,185)
(152,184);
s2 := Sym(227)!(  3,109)(  4,108)(  5,112)(  6,111)(  7,110)(  8,104)(  9,103)
( 10,107)( 11,106)( 12,105)( 13,124)( 14,123)( 15,127)( 16,126)( 17,125)
( 18,119)( 19,118)( 20,122)( 21,121)( 22,120)( 23,114)( 24,113)( 25,117)
( 26,116)( 27,115)( 28, 84)( 29, 83)( 30, 87)( 31, 86)( 32, 85)( 33, 79)
( 34, 78)( 35, 82)( 36, 81)( 37, 80)( 38, 99)( 39, 98)( 40,102)( 41,101)
( 42,100)( 43, 94)( 44, 93)( 45, 97)( 46, 96)( 47, 95)( 48, 89)( 49, 88)
( 50, 92)( 51, 91)( 52, 90)( 53,134)( 54,133)( 55,137)( 56,136)( 57,135)
( 58,129)( 59,128)( 60,132)( 61,131)( 62,130)( 63,149)( 64,148)( 65,152)
( 66,151)( 67,150)( 68,144)( 69,143)( 70,147)( 71,146)( 72,145)( 73,139)
( 74,138)( 75,142)( 76,141)( 77,140)(153,184)(154,183)(155,187)(156,186)
(157,185)(158,179)(159,178)(160,182)(161,181)(162,180)(163,199)(164,198)
(165,202)(166,201)(167,200)(168,194)(169,193)(170,197)(171,196)(172,195)
(173,189)(174,188)(175,192)(176,191)(177,190)(203,209)(204,208)(205,212)
(206,211)(207,210)(213,224)(214,223)(215,227)(216,226)(217,225)(218,219)
(220,222);
s3 := Sym(227)!(  4,  7)(  5,  6)(  9, 12)( 10, 11)( 14, 17)( 15, 16)( 19, 22)
( 20, 21)( 24, 27)( 25, 26)( 28, 53)( 29, 57)( 30, 56)( 31, 55)( 32, 54)
( 33, 58)( 34, 62)( 35, 61)( 36, 60)( 37, 59)( 38, 63)( 39, 67)( 40, 66)
( 41, 65)( 42, 64)( 43, 68)( 44, 72)( 45, 71)( 46, 70)( 47, 69)( 48, 73)
( 49, 77)( 50, 76)( 51, 75)( 52, 74)( 79, 82)( 80, 81)( 84, 87)( 85, 86)
( 89, 92)( 90, 91)( 94, 97)( 95, 96)( 99,102)(100,101)(103,128)(104,132)
(105,131)(106,130)(107,129)(108,133)(109,137)(110,136)(111,135)(112,134)
(113,138)(114,142)(115,141)(116,140)(117,139)(118,143)(119,147)(120,146)
(121,145)(122,144)(123,148)(124,152)(125,151)(126,150)(127,149)(154,157)
(155,156)(159,162)(160,161)(164,167)(165,166)(169,172)(170,171)(174,177)
(175,176)(178,203)(179,207)(180,206)(181,205)(182,204)(183,208)(184,212)
(185,211)(186,210)(187,209)(188,213)(189,217)(190,216)(191,215)(192,214)
(193,218)(194,222)(195,221)(196,220)(197,219)(198,223)(199,227)(200,226)
(201,225)(202,224);
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*s1*s2*s1*s2*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