Polytope of Type {30,15}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {30,15}*900
if this polytope has a name.
Group : SmallGroup(900,137)
Rank : 3
Schlafli Type : {30,15}
Number of vertices, edges, etc : 30, 225, 15
Order of s0s1s2 : 30
Order of s0s1s2s1 : 30
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {30,15,2} of size 1800
Vertex Figure Of :
   {2,30,15} of size 1800
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {10,15}*300
   5-fold quotients : {6,15}*180
   9-fold quotients : {10,5}*100
   15-fold quotients : {2,15}*60
   25-fold quotients : {6,3}*36
   45-fold quotients : {2,5}*20
   75-fold quotients : {2,3}*12
Covers (Minimal Covers in Boldface) :
   2-fold covers : {30,30}*1800h
Irregular Quotients (of which this is a minimal cover):
   None.

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);;
poly := Group([s0,s1,s2]);;
Finitely Presented Group Representation (GAP) : 
F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s2*s0*s1*s0*s1*s2*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(225)!(  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(225)!(  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(225)!(  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);
poly := sub<Sym(225)|s0,s1,s2>;
Finitely Presented Group Representation (Magma) : 
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s0*s1*s2*s0*s1*s0*s1*s2*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 >;
References : None.
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