Polytope of Type {30,30}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {30,30}*1800d
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 : 10
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, {10,30}*600c
   5-fold quotients : {6,30}*360b
   6-fold quotients : {10,15}*300
   9-fold quotients : {10,10}*200b
   15-fold quotients : {6,10}*120, {2,30}*120
   18-fold quotients : {10,5}*100
   25-fold quotients : {6,6}*72a
   30-fold quotients : {2,15}*60
   45-fold quotients : {2,10}*40
   75-fold quotients : {2,6}*24, {6,2}*24
   90-fold quotients : {2,5}*20
   150-fold quotients : {2,3}*12, {3,2}*12
   225-fold quotients : {2,2}*8
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)( 26,106)( 27,110)( 28,109)( 29,108)( 30,107)( 31,101)( 32,105)
( 33,104)( 34,103)( 35,102)( 36,121)( 37,125)( 38,124)( 39,123)( 40,122)
( 41,116)( 42,120)( 43,119)( 44,118)( 45,117)( 46,111)( 47,115)( 48,114)
( 49,113)( 50,112)( 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)(151,156)(152,160)(153,159)(154,158)(155,157)
(161,171)(162,175)(163,174)(164,173)(165,172)(167,170)(168,169)(176,181)
(177,185)(178,184)(179,183)(180,182)(186,196)(187,200)(188,199)(189,198)
(190,197)(192,195)(193,194)(201,206)(202,210)(203,209)(204,208)(205,207)
(211,221)(212,225)(213,224)(214,223)(215,222)(217,220)(218,219);;
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*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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*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)( 26,106)( 27,110)( 28,109)( 29,108)( 30,107)( 31,101)
( 32,105)( 33,104)( 34,103)( 35,102)( 36,121)( 37,125)( 38,124)( 39,123)
( 40,122)( 41,116)( 42,120)( 43,119)( 44,118)( 45,117)( 46,111)( 47,115)
( 48,114)( 49,113)( 50,112)( 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)(151,156)(152,160)(153,159)(154,158)
(155,157)(161,171)(162,175)(163,174)(164,173)(165,172)(167,170)(168,169)
(176,181)(177,185)(178,184)(179,183)(180,182)(186,196)(187,200)(188,199)
(189,198)(190,197)(192,195)(193,194)(201,206)(202,210)(203,209)(204,208)
(205,207)(211,221)(212,225)(213,224)(214,223)(215,222)(217,220)(218,219);
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*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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*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.
to this polytope