Polytope of Type {30,30}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {30,30}*1800b
if this polytope has a name.
Group : SmallGroup(1800,678)
Rank : 3
Schlafli Type : {30,30}
Number of vertices, edges, etc : 30, 450, 30
Order of s₀s₁s₂ : 30
Order of s₀s₁s₂s₁ : 30
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {30,10}*600a
   5-fold quotients : {6,30}*360a
   9-fold quotients : {10,10}*200b
   15-fold quotients : {6,10}*120
   18-fold quotients : {10,5}*100
   25-fold quotients : {6,6}*72c
   45-fold quotients : {2,10}*40
   50-fold quotients : {3,6}*36
   75-fold quotients : {6,2}*24
   90-fold quotients : {2,5}*20
   150-fold quotients : {3,2}*12
   225-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Irregular Quotients (of which this is a minimal cover):
   None.

Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope

Polytope of Type {30,30}

Twisty Puzzle