Polytope of Type {2,30,15}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,30,15}*1800
if this polytope has a name.
Group : SmallGroup(1800,736)
Rank : 4
Schlafli Type : {2,30,15}
Number of vertices, edges, etc : 2, 30, 225, 15
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 : {2,10,15}*600
   5-fold quotients : {2,6,15}*360
   9-fold quotients : {2,10,5}*200
   15-fold quotients : {2,2,15}*120
   25-fold quotients : {2,6,3}*72
   45-fold quotients : {2,2,5}*40
   75-fold quotients : {2,2,3}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

to this polytope