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Polytope of Type {30,15,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {30,15,2}*1800
if this polytope has a name.
Group : SmallGroup(1800,736)
Rank : 4
Schlafli Type : {30,15,2}
Number of vertices, edges, etc : 30, 225, 15, 2
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 : {10,15,2}*600
   5-fold quotients : {6,15,2}*360
   9-fold quotients : {10,5,2}*200
   15-fold quotients : {2,15,2}*120
   25-fold quotients : {6,3,2}*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 := (  2,  5)(  3,  4)(  7, 10)(  8,  9)( 12, 15)( 13, 14)( 17, 20)( 18, 19)
( 22, 25)( 23, 24)( 26, 51)( 27, 55)( 28, 54)( 29, 53)( 30, 52)( 31, 56)
( 32, 60)( 33, 59)( 34, 58)( 35, 57)( 36, 61)( 37, 65)( 38, 64)( 39, 63)
( 40, 62)( 41, 66)( 42, 70)( 43, 69)( 44, 68)( 45, 67)( 46, 71)( 47, 75)
( 48, 74)( 49, 73)( 50, 72)( 77, 80)( 78, 79)( 82, 85)( 83, 84)( 87, 90)
( 88, 89)( 92, 95)( 93, 94)( 97,100)( 98, 99)(101,126)(102,130)(103,129)
(104,128)(105,127)(106,131)(107,135)(108,134)(109,133)(110,132)(111,136)
(112,140)(113,139)(114,138)(115,137)(116,141)(117,145)(118,144)(119,143)
(120,142)(121,146)(122,150)(123,149)(124,148)(125,147)(152,155)(153,154)
(157,160)(158,159)(162,165)(163,164)(167,170)(168,169)(172,175)(173,174)
(176,201)(177,205)(178,204)(179,203)(180,202)(181,206)(182,210)(183,209)
(184,208)(185,207)(186,211)(187,215)(188,214)(189,213)(190,212)(191,216)
(192,220)(193,219)(194,218)(195,217)(196,221)(197,225)(198,224)(199,223)
(200,222);;
s1 := (  1, 27)(  2, 26)(  3, 30)(  4, 29)(  5, 28)(  6, 47)(  7, 46)(  8, 50)
(  9, 49)( 10, 48)( 11, 42)( 12, 41)( 13, 45)( 14, 44)( 15, 43)( 16, 37)
( 17, 36)( 18, 40)( 19, 39)( 20, 38)( 21, 32)( 22, 31)( 23, 35)( 24, 34)
( 25, 33)( 51, 52)( 53, 55)( 56, 72)( 57, 71)( 58, 75)( 59, 74)( 60, 73)
( 61, 67)( 62, 66)( 63, 70)( 64, 69)( 65, 68)( 76,177)( 77,176)( 78,180)
( 79,179)( 80,178)( 81,197)( 82,196)( 83,200)( 84,199)( 85,198)( 86,192)
( 87,191)( 88,195)( 89,194)( 90,193)( 91,187)( 92,186)( 93,190)( 94,189)
( 95,188)( 96,182)( 97,181)( 98,185)( 99,184)(100,183)(101,152)(102,151)
(103,155)(104,154)(105,153)(106,172)(107,171)(108,175)(109,174)(110,173)
(111,167)(112,166)(113,170)(114,169)(115,168)(116,162)(117,161)(118,165)
(119,164)(120,163)(121,157)(122,156)(123,160)(124,159)(125,158)(126,202)
(127,201)(128,205)(129,204)(130,203)(131,222)(132,221)(133,225)(134,224)
(135,223)(136,217)(137,216)(138,220)(139,219)(140,218)(141,212)(142,211)
(143,215)(144,214)(145,213)(146,207)(147,206)(148,210)(149,209)(150,208);;
s2 := (  1, 81)(  2, 85)(  3, 84)(  4, 83)(  5, 82)(  6, 76)(  7, 80)(  8, 79)
(  9, 78)( 10, 77)( 11, 96)( 12,100)( 13, 99)( 14, 98)( 15, 97)( 16, 91)
( 17, 95)( 18, 94)( 19, 93)( 20, 92)( 21, 86)( 22, 90)( 23, 89)( 24, 88)
( 25, 87)( 26,131)( 27,135)( 28,134)( 29,133)( 30,132)( 31,126)( 32,130)
( 33,129)( 34,128)( 35,127)( 36,146)( 37,150)( 38,149)( 39,148)( 40,147)
( 41,141)( 42,145)( 43,144)( 44,143)( 45,142)( 46,136)( 47,140)( 48,139)
( 49,138)( 50,137)( 51,106)( 52,110)( 53,109)( 54,108)( 55,107)( 56,101)
( 57,105)( 58,104)( 59,103)( 60,102)( 61,121)( 62,125)( 63,124)( 64,123)
( 65,122)( 66,116)( 67,120)( 68,119)( 69,118)( 70,117)( 71,111)( 72,115)
( 73,114)( 74,113)( 75,112)(151,156)(152,160)(153,159)(154,158)(155,157)
(161,171)(162,175)(163,174)(164,173)(165,172)(167,170)(168,169)(176,206)
(177,210)(178,209)(179,208)(180,207)(181,201)(182,205)(183,204)(184,203)
(185,202)(186,221)(187,225)(188,224)(189,223)(190,222)(191,216)(192,220)
(193,219)(194,218)(195,217)(196,211)(197,215)(198,214)(199,213)(200,212);;
s3 := (226,227);;
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*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s2*s0*s1*s0*s1*s2*s0*s1*s0*s1, 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)!(  2,  5)(  3,  4)(  7, 10)(  8,  9)( 12, 15)( 13, 14)( 17, 20)
( 18, 19)( 22, 25)( 23, 24)( 26, 51)( 27, 55)( 28, 54)( 29, 53)( 30, 52)
( 31, 56)( 32, 60)( 33, 59)( 34, 58)( 35, 57)( 36, 61)( 37, 65)( 38, 64)
( 39, 63)( 40, 62)( 41, 66)( 42, 70)( 43, 69)( 44, 68)( 45, 67)( 46, 71)
( 47, 75)( 48, 74)( 49, 73)( 50, 72)( 77, 80)( 78, 79)( 82, 85)( 83, 84)
( 87, 90)( 88, 89)( 92, 95)( 93, 94)( 97,100)( 98, 99)(101,126)(102,130)
(103,129)(104,128)(105,127)(106,131)(107,135)(108,134)(109,133)(110,132)
(111,136)(112,140)(113,139)(114,138)(115,137)(116,141)(117,145)(118,144)
(119,143)(120,142)(121,146)(122,150)(123,149)(124,148)(125,147)(152,155)
(153,154)(157,160)(158,159)(162,165)(163,164)(167,170)(168,169)(172,175)
(173,174)(176,201)(177,205)(178,204)(179,203)(180,202)(181,206)(182,210)
(183,209)(184,208)(185,207)(186,211)(187,215)(188,214)(189,213)(190,212)
(191,216)(192,220)(193,219)(194,218)(195,217)(196,221)(197,225)(198,224)
(199,223)(200,222);
s1 := Sym(227)!(  1, 27)(  2, 26)(  3, 30)(  4, 29)(  5, 28)(  6, 47)(  7, 46)
(  8, 50)(  9, 49)( 10, 48)( 11, 42)( 12, 41)( 13, 45)( 14, 44)( 15, 43)
( 16, 37)( 17, 36)( 18, 40)( 19, 39)( 20, 38)( 21, 32)( 22, 31)( 23, 35)
( 24, 34)( 25, 33)( 51, 52)( 53, 55)( 56, 72)( 57, 71)( 58, 75)( 59, 74)
( 60, 73)( 61, 67)( 62, 66)( 63, 70)( 64, 69)( 65, 68)( 76,177)( 77,176)
( 78,180)( 79,179)( 80,178)( 81,197)( 82,196)( 83,200)( 84,199)( 85,198)
( 86,192)( 87,191)( 88,195)( 89,194)( 90,193)( 91,187)( 92,186)( 93,190)
( 94,189)( 95,188)( 96,182)( 97,181)( 98,185)( 99,184)(100,183)(101,152)
(102,151)(103,155)(104,154)(105,153)(106,172)(107,171)(108,175)(109,174)
(110,173)(111,167)(112,166)(113,170)(114,169)(115,168)(116,162)(117,161)
(118,165)(119,164)(120,163)(121,157)(122,156)(123,160)(124,159)(125,158)
(126,202)(127,201)(128,205)(129,204)(130,203)(131,222)(132,221)(133,225)
(134,224)(135,223)(136,217)(137,216)(138,220)(139,219)(140,218)(141,212)
(142,211)(143,215)(144,214)(145,213)(146,207)(147,206)(148,210)(149,209)
(150,208);
s2 := Sym(227)!(  1, 81)(  2, 85)(  3, 84)(  4, 83)(  5, 82)(  6, 76)(  7, 80)
(  8, 79)(  9, 78)( 10, 77)( 11, 96)( 12,100)( 13, 99)( 14, 98)( 15, 97)
( 16, 91)( 17, 95)( 18, 94)( 19, 93)( 20, 92)( 21, 86)( 22, 90)( 23, 89)
( 24, 88)( 25, 87)( 26,131)( 27,135)( 28,134)( 29,133)( 30,132)( 31,126)
( 32,130)( 33,129)( 34,128)( 35,127)( 36,146)( 37,150)( 38,149)( 39,148)
( 40,147)( 41,141)( 42,145)( 43,144)( 44,143)( 45,142)( 46,136)( 47,140)
( 48,139)( 49,138)( 50,137)( 51,106)( 52,110)( 53,109)( 54,108)( 55,107)
( 56,101)( 57,105)( 58,104)( 59,103)( 60,102)( 61,121)( 62,125)( 63,124)
( 64,123)( 65,122)( 66,116)( 67,120)( 68,119)( 69,118)( 70,117)( 71,111)
( 72,115)( 73,114)( 74,113)( 75,112)(151,156)(152,160)(153,159)(154,158)
(155,157)(161,171)(162,175)(163,174)(164,173)(165,172)(167,170)(168,169)
(176,206)(177,210)(178,209)(179,208)(180,207)(181,201)(182,205)(183,204)
(184,203)(185,202)(186,221)(187,225)(188,224)(189,223)(190,222)(191,216)
(192,220)(193,219)(194,218)(195,217)(196,211)(197,215)(198,214)(199,213)
(200,212);
s3 := Sym(227)!(226,227);
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*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s2*s0*s1*s0*s1*s2*s0*s1*s0*s1, 
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 >; 
 

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