Polytope of Type {2,10,46}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,10,46}*1840
if this polytope has a name.
Group : SmallGroup(1840,174)
Rank : 4
Schlafli Type : {2,10,46}
Number of vertices, edges, etc : 2, 10, 230, 46
Order of s₀s₁s₂s₃ : 230
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   5-fold quotients : {2,2,46}*368
   10-fold quotients : {2,2,23}*184
   23-fold quotients : {2,10,2}*80
   46-fold quotients : {2,5,2}*40
   115-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := ( 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)( 47,116)( 48,117)( 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)( 70, 93)( 71, 94)(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)(162,231)(163,232)(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)(185,208)(186,209);;
s2 := (  3, 26)(  4, 48)(  5, 47)(  6, 46)(  7, 45)(  8, 44)(  9, 43)( 10, 42)
( 11, 41)( 12, 40)( 13, 39)( 14, 38)( 15, 37)( 16, 36)( 17, 35)( 18, 34)
( 19, 33)( 20, 32)( 21, 31)( 22, 30)( 23, 29)( 24, 28)( 25, 27)( 49, 95)
( 50,117)( 51,116)( 52,115)( 53,114)( 54,113)( 55,112)( 56,111)( 57,110)
( 58,109)( 59,108)( 60,107)( 61,106)( 62,105)( 63,104)( 64,103)( 65,102)
( 66,101)( 67,100)( 68, 99)( 69, 98)( 70, 97)( 71, 96)( 73, 94)( 74, 93)
( 75, 92)( 76, 91)( 77, 90)( 78, 89)( 79, 88)( 80, 87)( 81, 86)( 82, 85)
( 83, 84)(118,141)(119,163)(120,162)(121,161)(122,160)(123,159)(124,158)
(125,157)(126,156)(127,155)(128,154)(129,153)(130,152)(131,151)(132,150)
(133,149)(134,148)(135,147)(136,146)(137,145)(138,144)(139,143)(140,142)
(164,210)(165,232)(166,231)(167,230)(168,229)(169,228)(170,227)(171,226)
(172,225)(173,224)(174,223)(175,222)(176,221)(177,220)(178,219)(179,218)
(180,217)(181,216)(182,215)(183,214)(184,213)(185,212)(186,211)(188,209)
(189,208)(190,207)(191,206)(192,205)(193,204)(194,203)(195,202)(196,201)
(197,200)(198,199);;
s3 := (  3,119)(  4,118)(  5,140)(  6,139)(  7,138)(  8,137)(  9,136)( 10,135)
( 11,134)( 12,133)( 13,132)( 14,131)( 15,130)( 16,129)( 17,128)( 18,127)
( 19,126)( 20,125)( 21,124)( 22,123)( 23,122)( 24,121)( 25,120)( 26,142)
( 27,141)( 28,163)( 29,162)( 30,161)( 31,160)( 32,159)( 33,158)( 34,157)
( 35,156)( 36,155)( 37,154)( 38,153)( 39,152)( 40,151)( 41,150)( 42,149)
( 43,148)( 44,147)( 45,146)( 46,145)( 47,144)( 48,143)( 49,165)( 50,164)
( 51,186)( 52,185)( 53,184)( 54,183)( 55,182)( 56,181)( 57,180)( 58,179)
( 59,178)( 60,177)( 61,176)( 62,175)( 63,174)( 64,173)( 65,172)( 66,171)
( 67,170)( 68,169)( 69,168)( 70,167)( 71,166)( 72,188)( 73,187)( 74,209)
( 75,208)( 76,207)( 77,206)( 78,205)( 79,204)( 80,203)( 81,202)( 82,201)
( 83,200)( 84,199)( 85,198)( 86,197)( 87,196)( 88,195)( 89,194)( 90,193)
( 91,192)( 92,191)( 93,190)( 94,189)( 95,211)( 96,210)( 97,232)( 98,231)
( 99,230)(100,229)(101,228)(102,227)(103,226)(104,225)(105,224)(106,223)
(107,222)(108,221)(109,220)(110,219)(111,218)(112,217)(113,216)(114,215)
(115,214)(116,213)(117,212);;
poly := Group([s0,s1,s2,s3]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s1*s2*s3*s2*s1*s2*s3*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(232)!(1,2);
s1 := Sym(232)!( 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)( 47,116)( 48,117)
( 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)( 70, 93)( 71, 94)(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)(162,231)(163,232)(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)(185,208)(186,209);
s2 := Sym(232)!(  3, 26)(  4, 48)(  5, 47)(  6, 46)(  7, 45)(  8, 44)(  9, 43)
( 10, 42)( 11, 41)( 12, 40)( 13, 39)( 14, 38)( 15, 37)( 16, 36)( 17, 35)
( 18, 34)( 19, 33)( 20, 32)( 21, 31)( 22, 30)( 23, 29)( 24, 28)( 25, 27)
( 49, 95)( 50,117)( 51,116)( 52,115)( 53,114)( 54,113)( 55,112)( 56,111)
( 57,110)( 58,109)( 59,108)( 60,107)( 61,106)( 62,105)( 63,104)( 64,103)
( 65,102)( 66,101)( 67,100)( 68, 99)( 69, 98)( 70, 97)( 71, 96)( 73, 94)
( 74, 93)( 75, 92)( 76, 91)( 77, 90)( 78, 89)( 79, 88)( 80, 87)( 81, 86)
( 82, 85)( 83, 84)(118,141)(119,163)(120,162)(121,161)(122,160)(123,159)
(124,158)(125,157)(126,156)(127,155)(128,154)(129,153)(130,152)(131,151)
(132,150)(133,149)(134,148)(135,147)(136,146)(137,145)(138,144)(139,143)
(140,142)(164,210)(165,232)(166,231)(167,230)(168,229)(169,228)(170,227)
(171,226)(172,225)(173,224)(174,223)(175,222)(176,221)(177,220)(178,219)
(179,218)(180,217)(181,216)(182,215)(183,214)(184,213)(185,212)(186,211)
(188,209)(189,208)(190,207)(191,206)(192,205)(193,204)(194,203)(195,202)
(196,201)(197,200)(198,199);
s3 := Sym(232)!(  3,119)(  4,118)(  5,140)(  6,139)(  7,138)(  8,137)(  9,136)
( 10,135)( 11,134)( 12,133)( 13,132)( 14,131)( 15,130)( 16,129)( 17,128)
( 18,127)( 19,126)( 20,125)( 21,124)( 22,123)( 23,122)( 24,121)( 25,120)
( 26,142)( 27,141)( 28,163)( 29,162)( 30,161)( 31,160)( 32,159)( 33,158)
( 34,157)( 35,156)( 36,155)( 37,154)( 38,153)( 39,152)( 40,151)( 41,150)
( 42,149)( 43,148)( 44,147)( 45,146)( 46,145)( 47,144)( 48,143)( 49,165)
( 50,164)( 51,186)( 52,185)( 53,184)( 54,183)( 55,182)( 56,181)( 57,180)
( 58,179)( 59,178)( 60,177)( 61,176)( 62,175)( 63,174)( 64,173)( 65,172)
( 66,171)( 67,170)( 68,169)( 69,168)( 70,167)( 71,166)( 72,188)( 73,187)
( 74,209)( 75,208)( 76,207)( 77,206)( 78,205)( 79,204)( 80,203)( 81,202)
( 82,201)( 83,200)( 84,199)( 85,198)( 86,197)( 87,196)( 88,195)( 89,194)
( 90,193)( 91,192)( 92,191)( 93,190)( 94,189)( 95,211)( 96,210)( 97,232)
( 98,231)( 99,230)(100,229)(101,228)(102,227)(103,226)(104,225)(105,224)
(106,223)(107,222)(108,221)(109,220)(110,219)(111,218)(112,217)(113,216)
(114,215)(115,214)(116,213)(117,212);
poly := sub<Sym(232)|s0,s1,s2,s3>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s1*s2*s3*s2*s1*s2*s3*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

to this polytope