Polytope of Type {10,46}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,46}*920
Also Known As : {10,46|2}. if this polytope has another name.
Group : SmallGroup(920,35)
Rank : 3
Schlafli Type : {10,46}
Number of vertices, edges, etc : 10, 230, 46
Order of s₀s₁s₂ : 230
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {10,46,2} of size 1840
Vertex Figure Of :
   {2,10,46} of size 1840
Quotients (Maximal Quotients in Boldface) :
   5-fold quotients : {2,46}*184
   10-fold quotients : {2,23}*92
   23-fold quotients : {10,2}*40
   46-fold quotients : {5,2}*20
   115-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {20,46}*1840, {10,92}*1840
Permutation Representation (GAP) :

s0 := ( 24, 93)( 25, 94)( 26, 95)( 27, 96)( 28, 97)( 29, 98)( 30, 99)( 31,100)
( 32,101)( 33,102)( 34,103)( 35,104)( 36,105)( 37,106)( 38,107)( 39,108)
( 40,109)( 41,110)( 42,111)( 43,112)( 44,113)( 45,114)( 46,115)( 47, 70)
( 48, 71)( 49, 72)( 50, 73)( 51, 74)( 52, 75)( 53, 76)( 54, 77)( 55, 78)
( 56, 79)( 57, 80)( 58, 81)( 59, 82)( 60, 83)( 61, 84)( 62, 85)( 63, 86)
( 64, 87)( 65, 88)( 66, 89)( 67, 90)( 68, 91)( 69, 92)(139,208)(140,209)
(141,210)(142,211)(143,212)(144,213)(145,214)(146,215)(147,216)(148,217)
(149,218)(150,219)(151,220)(152,221)(153,222)(154,223)(155,224)(156,225)
(157,226)(158,227)(159,228)(160,229)(161,230)(162,185)(163,186)(164,187)
(165,188)(166,189)(167,190)(168,191)(169,192)(170,193)(171,194)(172,195)
(173,196)(174,197)(175,198)(176,199)(177,200)(178,201)(179,202)(180,203)
(181,204)(182,205)(183,206)(184,207);;
s1 := (  1, 24)(  2, 46)(  3, 45)(  4, 44)(  5, 43)(  6, 42)(  7, 41)(  8, 40)
(  9, 39)( 10, 38)( 11, 37)( 12, 36)( 13, 35)( 14, 34)( 15, 33)( 16, 32)
( 17, 31)( 18, 30)( 19, 29)( 20, 28)( 21, 27)( 22, 26)( 23, 25)( 47, 93)
( 48,115)( 49,114)( 50,113)( 51,112)( 52,111)( 53,110)( 54,109)( 55,108)
( 56,107)( 57,106)( 58,105)( 59,104)( 60,103)( 61,102)( 62,101)( 63,100)
( 64, 99)( 65, 98)( 66, 97)( 67, 96)( 68, 95)( 69, 94)( 71, 92)( 72, 91)
( 73, 90)( 74, 89)( 75, 88)( 76, 87)( 77, 86)( 78, 85)( 79, 84)( 80, 83)
( 81, 82)(116,139)(117,161)(118,160)(119,159)(120,158)(121,157)(122,156)
(123,155)(124,154)(125,153)(126,152)(127,151)(128,150)(129,149)(130,148)
(131,147)(132,146)(133,145)(134,144)(135,143)(136,142)(137,141)(138,140)
(162,208)(163,230)(164,229)(165,228)(166,227)(167,226)(168,225)(169,224)
(170,223)(171,222)(172,221)(173,220)(174,219)(175,218)(176,217)(177,216)
(178,215)(179,214)(180,213)(181,212)(182,211)(183,210)(184,209)(186,207)
(187,206)(188,205)(189,204)(190,203)(191,202)(192,201)(193,200)(194,199)
(195,198)(196,197);;
s2 := (  1,117)(  2,116)(  3,138)(  4,137)(  5,136)(  6,135)(  7,134)(  8,133)
(  9,132)( 10,131)( 11,130)( 12,129)( 13,128)( 14,127)( 15,126)( 16,125)
( 17,124)( 18,123)( 19,122)( 20,121)( 21,120)( 22,119)( 23,118)( 24,140)
( 25,139)( 26,161)( 27,160)( 28,159)( 29,158)( 30,157)( 31,156)( 32,155)
( 33,154)( 34,153)( 35,152)( 36,151)( 37,150)( 38,149)( 39,148)( 40,147)
( 41,146)( 42,145)( 43,144)( 44,143)( 45,142)( 46,141)( 47,163)( 48,162)
( 49,184)( 50,183)( 51,182)( 52,181)( 53,180)( 54,179)( 55,178)( 56,177)
( 57,176)( 58,175)( 59,174)( 60,173)( 61,172)( 62,171)( 63,170)( 64,169)
( 65,168)( 66,167)( 67,166)( 68,165)( 69,164)( 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)( 93,209)( 94,208)( 95,230)( 96,229)
( 97,228)( 98,227)( 99,226)(100,225)(101,224)(102,223)(103,222)(104,221)
(105,220)(106,219)(107,218)(108,217)(109,216)(110,215)(111,214)(112,213)
(113,212)(114,211)(115,210);;
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*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*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*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(230)!( 24, 93)( 25, 94)( 26, 95)( 27, 96)( 28, 97)( 29, 98)( 30, 99)
( 31,100)( 32,101)( 33,102)( 34,103)( 35,104)( 36,105)( 37,106)( 38,107)
( 39,108)( 40,109)( 41,110)( 42,111)( 43,112)( 44,113)( 45,114)( 46,115)
( 47, 70)( 48, 71)( 49, 72)( 50, 73)( 51, 74)( 52, 75)( 53, 76)( 54, 77)
( 55, 78)( 56, 79)( 57, 80)( 58, 81)( 59, 82)( 60, 83)( 61, 84)( 62, 85)
( 63, 86)( 64, 87)( 65, 88)( 66, 89)( 67, 90)( 68, 91)( 69, 92)(139,208)
(140,209)(141,210)(142,211)(143,212)(144,213)(145,214)(146,215)(147,216)
(148,217)(149,218)(150,219)(151,220)(152,221)(153,222)(154,223)(155,224)
(156,225)(157,226)(158,227)(159,228)(160,229)(161,230)(162,185)(163,186)
(164,187)(165,188)(166,189)(167,190)(168,191)(169,192)(170,193)(171,194)
(172,195)(173,196)(174,197)(175,198)(176,199)(177,200)(178,201)(179,202)
(180,203)(181,204)(182,205)(183,206)(184,207);
s1 := Sym(230)!(  1, 24)(  2, 46)(  3, 45)(  4, 44)(  5, 43)(  6, 42)(  7, 41)
(  8, 40)(  9, 39)( 10, 38)( 11, 37)( 12, 36)( 13, 35)( 14, 34)( 15, 33)
( 16, 32)( 17, 31)( 18, 30)( 19, 29)( 20, 28)( 21, 27)( 22, 26)( 23, 25)
( 47, 93)( 48,115)( 49,114)( 50,113)( 51,112)( 52,111)( 53,110)( 54,109)
( 55,108)( 56,107)( 57,106)( 58,105)( 59,104)( 60,103)( 61,102)( 62,101)
( 63,100)( 64, 99)( 65, 98)( 66, 97)( 67, 96)( 68, 95)( 69, 94)( 71, 92)
( 72, 91)( 73, 90)( 74, 89)( 75, 88)( 76, 87)( 77, 86)( 78, 85)( 79, 84)
( 80, 83)( 81, 82)(116,139)(117,161)(118,160)(119,159)(120,158)(121,157)
(122,156)(123,155)(124,154)(125,153)(126,152)(127,151)(128,150)(129,149)
(130,148)(131,147)(132,146)(133,145)(134,144)(135,143)(136,142)(137,141)
(138,140)(162,208)(163,230)(164,229)(165,228)(166,227)(167,226)(168,225)
(169,224)(170,223)(171,222)(172,221)(173,220)(174,219)(175,218)(176,217)
(177,216)(178,215)(179,214)(180,213)(181,212)(182,211)(183,210)(184,209)
(186,207)(187,206)(188,205)(189,204)(190,203)(191,202)(192,201)(193,200)
(194,199)(195,198)(196,197);
s2 := Sym(230)!(  1,117)(  2,116)(  3,138)(  4,137)(  5,136)(  6,135)(  7,134)
(  8,133)(  9,132)( 10,131)( 11,130)( 12,129)( 13,128)( 14,127)( 15,126)
( 16,125)( 17,124)( 18,123)( 19,122)( 20,121)( 21,120)( 22,119)( 23,118)
( 24,140)( 25,139)( 26,161)( 27,160)( 28,159)( 29,158)( 30,157)( 31,156)
( 32,155)( 33,154)( 34,153)( 35,152)( 36,151)( 37,150)( 38,149)( 39,148)
( 40,147)( 41,146)( 42,145)( 43,144)( 44,143)( 45,142)( 46,141)( 47,163)
( 48,162)( 49,184)( 50,183)( 51,182)( 52,181)( 53,180)( 54,179)( 55,178)
( 56,177)( 57,176)( 58,175)( 59,174)( 60,173)( 61,172)( 62,171)( 63,170)
( 64,169)( 65,168)( 66,167)( 67,166)( 68,165)( 69,164)( 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)( 93,209)( 94,208)( 95,230)
( 96,229)( 97,228)( 98,227)( 99,226)(100,225)(101,224)(102,223)(103,222)
(104,221)(105,220)(106,219)(107,218)(108,217)(109,216)(110,215)(111,214)
(112,213)(113,212)(114,211)(115,210);
poly := sub<Sym(230)|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*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*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*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