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Polytope of Type {230}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {230}*460
Also Known As : 230-gon, {230}. if this polytope has another name.
Group : SmallGroup(460,10)
Rank : 2
Schlafli Type : {230}
Number of vertices, edges, etc : 230, 230
Order of s0s1 : 230
Special Properties :
   Universal
   Spherical
   Locally Spherical
   Orientable
   Self-Dual
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {230,2} of size 920
   {230,4} of size 1840
Vertex Figure Of :
   {2,230} of size 920
   {4,230} of size 1840
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {115}*230
   5-fold quotients : {46}*92
   10-fold quotients : {23}*46
   23-fold quotients : {10}*20
   46-fold quotients : {5}*10
   115-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   2-fold covers : {460}*920
   3-fold covers : {690}*1380
   4-fold covers : {920}*1840
Permutation Representation (GAP) :
s0 := (  2, 23)(  3, 22)(  4, 21)(  5, 20)(  6, 19)(  7, 18)(  8, 17)(  9, 16)
( 10, 15)( 11, 14)( 12, 13)( 24, 93)( 25,115)( 26,114)( 27,113)( 28,112)
( 29,111)( 30,110)( 31,109)( 32,108)( 33,107)( 34,106)( 35,105)( 36,104)
( 37,103)( 38,102)( 39,101)( 40,100)( 41, 99)( 42, 98)( 43, 97)( 44, 96)
( 45, 95)( 46, 94)( 47, 70)( 48, 92)( 49, 91)( 50, 90)( 51, 89)( 52, 88)
( 53, 87)( 54, 86)( 55, 85)( 56, 84)( 57, 83)( 58, 82)( 59, 81)( 60, 80)
( 61, 79)( 62, 78)( 63, 77)( 64, 76)( 65, 75)( 66, 74)( 67, 73)( 68, 72)
( 69, 71)(117,138)(118,137)(119,136)(120,135)(121,134)(122,133)(123,132)
(124,131)(125,130)(126,129)(127,128)(139,208)(140,230)(141,229)(142,228)
(143,227)(144,226)(145,225)(146,224)(147,223)(148,222)(149,221)(150,220)
(151,219)(152,218)(153,217)(154,216)(155,215)(156,214)(157,213)(158,212)
(159,211)(160,210)(161,209)(162,185)(163,207)(164,206)(165,205)(166,204)
(167,203)(168,202)(169,201)(170,200)(171,199)(172,198)(173,197)(174,196)
(175,195)(176,194)(177,193)(178,192)(179,191)(180,190)(181,189)(182,188)
(183,187)(184,186);;
s1 := (  1,140)(  2,139)(  3,161)(  4,160)(  5,159)(  6,158)(  7,157)(  8,156)
(  9,155)( 10,154)( 11,153)( 12,152)( 13,151)( 14,150)( 15,149)( 16,148)
( 17,147)( 18,146)( 19,145)( 20,144)( 21,143)( 22,142)( 23,141)( 24,117)
( 25,116)( 26,138)( 27,137)( 28,136)( 29,135)( 30,134)( 31,133)( 32,132)
( 33,131)( 34,130)( 35,129)( 36,128)( 37,127)( 38,126)( 39,125)( 40,124)
( 41,123)( 42,122)( 43,121)( 44,120)( 45,119)( 46,118)( 47,209)( 48,208)
( 49,230)( 50,229)( 51,228)( 52,227)( 53,226)( 54,225)( 55,224)( 56,223)
( 57,222)( 58,221)( 59,220)( 60,219)( 61,218)( 62,217)( 63,216)( 64,215)
( 65,214)( 66,213)( 67,212)( 68,211)( 69,210)( 70,186)( 71,185)( 72,207)
( 73,206)( 74,205)( 75,204)( 76,203)( 77,202)( 78,201)( 79,200)( 80,199)
( 81,198)( 82,197)( 83,196)( 84,195)( 85,194)( 86,193)( 87,192)( 88,191)
( 89,190)( 90,189)( 91,188)( 92,187)( 93,163)( 94,162)( 95,184)( 96,183)
( 97,182)( 98,181)( 99,180)(100,179)(101,178)(102,177)(103,176)(104,175)
(105,174)(106,173)(107,172)(108,171)(109,170)(110,169)(111,168)(112,167)
(113,166)(114,165)(115,164);;
poly := Group([s0,s1]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1");;
s0 := F.1;;  s1 := F.2;;  
rels := [ s0*s0, s1*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*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*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*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*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*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*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*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(230)!(  2, 23)(  3, 22)(  4, 21)(  5, 20)(  6, 19)(  7, 18)(  8, 17)
(  9, 16)( 10, 15)( 11, 14)( 12, 13)( 24, 93)( 25,115)( 26,114)( 27,113)
( 28,112)( 29,111)( 30,110)( 31,109)( 32,108)( 33,107)( 34,106)( 35,105)
( 36,104)( 37,103)( 38,102)( 39,101)( 40,100)( 41, 99)( 42, 98)( 43, 97)
( 44, 96)( 45, 95)( 46, 94)( 47, 70)( 48, 92)( 49, 91)( 50, 90)( 51, 89)
( 52, 88)( 53, 87)( 54, 86)( 55, 85)( 56, 84)( 57, 83)( 58, 82)( 59, 81)
( 60, 80)( 61, 79)( 62, 78)( 63, 77)( 64, 76)( 65, 75)( 66, 74)( 67, 73)
( 68, 72)( 69, 71)(117,138)(118,137)(119,136)(120,135)(121,134)(122,133)
(123,132)(124,131)(125,130)(126,129)(127,128)(139,208)(140,230)(141,229)
(142,228)(143,227)(144,226)(145,225)(146,224)(147,223)(148,222)(149,221)
(150,220)(151,219)(152,218)(153,217)(154,216)(155,215)(156,214)(157,213)
(158,212)(159,211)(160,210)(161,209)(162,185)(163,207)(164,206)(165,205)
(166,204)(167,203)(168,202)(169,201)(170,200)(171,199)(172,198)(173,197)
(174,196)(175,195)(176,194)(177,193)(178,192)(179,191)(180,190)(181,189)
(182,188)(183,187)(184,186);
s1 := Sym(230)!(  1,140)(  2,139)(  3,161)(  4,160)(  5,159)(  6,158)(  7,157)
(  8,156)(  9,155)( 10,154)( 11,153)( 12,152)( 13,151)( 14,150)( 15,149)
( 16,148)( 17,147)( 18,146)( 19,145)( 20,144)( 21,143)( 22,142)( 23,141)
( 24,117)( 25,116)( 26,138)( 27,137)( 28,136)( 29,135)( 30,134)( 31,133)
( 32,132)( 33,131)( 34,130)( 35,129)( 36,128)( 37,127)( 38,126)( 39,125)
( 40,124)( 41,123)( 42,122)( 43,121)( 44,120)( 45,119)( 46,118)( 47,209)
( 48,208)( 49,230)( 50,229)( 51,228)( 52,227)( 53,226)( 54,225)( 55,224)
( 56,223)( 57,222)( 58,221)( 59,220)( 60,219)( 61,218)( 62,217)( 63,216)
( 64,215)( 65,214)( 66,213)( 67,212)( 68,211)( 69,210)( 70,186)( 71,185)
( 72,207)( 73,206)( 74,205)( 75,204)( 76,203)( 77,202)( 78,201)( 79,200)
( 80,199)( 81,198)( 82,197)( 83,196)( 84,195)( 85,194)( 86,193)( 87,192)
( 88,191)( 89,190)( 90,189)( 91,188)( 92,187)( 93,163)( 94,162)( 95,184)
( 96,183)( 97,182)( 98,181)( 99,180)(100,179)(101,178)(102,177)(103,176)
(104,175)(105,174)(106,173)(107,172)(108,171)(109,170)(110,169)(111,168)
(112,167)(113,166)(114,165)(115,164);
poly := sub<Sym(230)|s0,s1>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1> := Group< s0,s1 | s0*s0, s1*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*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*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*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*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*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*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*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