Polytope of Type {30,30}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {30,30}*1800a
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 : 6
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}*600b
   5-fold quotients : {6,30}*360a, {30,6}*360c
   9-fold quotients : {10,10}*200a
   10-fold quotients : {15,6}*180
   15-fold quotients : {6,10}*120, {30,2}*120
   25-fold quotients : {6,6}*72c
   30-fold quotients : {15,2}*60
   45-fold quotients : {2,10}*40, {10,2}*40
   50-fold quotients : {3,6}*36
   75-fold quotients : {6,2}*24
   90-fold quotients : {2,5}*20, {5,2}*20
   150-fold quotients : {3,2}*12
   225-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
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,  7)(  8, 10)( 11, 12)( 13, 15)( 16, 17)( 18, 20)
( 21, 22)( 23, 25)( 26, 52)( 27, 51)( 28, 55)( 29, 54)( 30, 53)( 31, 57)
( 32, 56)( 33, 60)( 34, 59)( 35, 58)( 36, 62)( 37, 61)( 38, 65)( 39, 64)
( 40, 63)( 41, 67)( 42, 66)( 43, 70)( 44, 69)( 45, 68)( 46, 72)( 47, 71)
( 48, 75)( 49, 74)( 50, 73)( 76, 77)( 78, 80)( 81, 82)( 83, 85)( 86, 87)
( 88, 90)( 91, 92)( 93, 95)( 96, 97)( 98,100)(101,127)(102,126)(103,130)
(104,129)(105,128)(106,132)(107,131)(108,135)(109,134)(110,133)(111,137)
(112,136)(113,140)(114,139)(115,138)(116,142)(117,141)(118,145)(119,144)
(120,143)(121,147)(122,146)(123,150)(124,149)(125,148)(151,152)(153,155)
(156,157)(158,160)(161,162)(163,165)(166,167)(168,170)(171,172)(173,175)
(176,202)(177,201)(178,205)(179,204)(180,203)(181,207)(182,206)(183,210)
(184,209)(185,208)(186,212)(187,211)(188,215)(189,214)(190,213)(191,217)
(192,216)(193,220)(194,219)(195,218)(196,222)(197,221)(198,225)(199,224)
(200,223);;
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, s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1, 
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*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*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,  7)(  8, 10)( 11, 12)( 13, 15)( 16, 17)
( 18, 20)( 21, 22)( 23, 25)( 26, 52)( 27, 51)( 28, 55)( 29, 54)( 30, 53)
( 31, 57)( 32, 56)( 33, 60)( 34, 59)( 35, 58)( 36, 62)( 37, 61)( 38, 65)
( 39, 64)( 40, 63)( 41, 67)( 42, 66)( 43, 70)( 44, 69)( 45, 68)( 46, 72)
( 47, 71)( 48, 75)( 49, 74)( 50, 73)( 76, 77)( 78, 80)( 81, 82)( 83, 85)
( 86, 87)( 88, 90)( 91, 92)( 93, 95)( 96, 97)( 98,100)(101,127)(102,126)
(103,130)(104,129)(105,128)(106,132)(107,131)(108,135)(109,134)(110,133)
(111,137)(112,136)(113,140)(114,139)(115,138)(116,142)(117,141)(118,145)
(119,144)(120,143)(121,147)(122,146)(123,150)(124,149)(125,148)(151,152)
(153,155)(156,157)(158,160)(161,162)(163,165)(166,167)(168,170)(171,172)
(173,175)(176,202)(177,201)(178,205)(179,204)(180,203)(181,207)(182,206)
(183,210)(184,209)(185,208)(186,212)(187,211)(188,215)(189,214)(190,213)
(191,217)(192,216)(193,220)(194,219)(195,218)(196,222)(197,221)(198,225)
(199,224)(200,223);
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, s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1, 
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*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*s0*s1 >;

References : None.
to this polytope