Polytope of Type {2,46,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,46,10}*1840
if this polytope has a name.
Group : SmallGroup(1840,174)
Rank : 4
Schlafli Type : {2,46,10}
Number of vertices, edges, etc : 2, 46, 230, 10
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 : {2,46,2}*368
   10-fold quotients : {2,23,2}*184
   23-fold quotients : {2,2,10}*80
   46-fold quotients : {2,2,5}*40
   115-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

to this polytope