Polytope of Type {46,10,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {46,10,2}*1840
if this polytope has a name.
Group : SmallGroup(1840,174)
Rank : 4
Schlafli Type : {46,10,2}
Number of vertices, edges, etc : 46, 230, 10, 2
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 : {46,2,2}*368
   10-fold quotients : {23,2,2}*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 := (  2, 23)(  3, 22)(  4, 21)(  5, 20)(  6, 19)(  7, 18)(  8, 17)(  9, 16)
( 10, 15)( 11, 14)( 12, 13)( 25, 46)( 26, 45)( 27, 44)( 28, 43)( 29, 42)
( 30, 41)( 31, 40)( 32, 39)( 33, 38)( 34, 37)( 35, 36)( 48, 69)( 49, 68)
( 50, 67)( 51, 66)( 52, 65)( 53, 64)( 54, 63)( 55, 62)( 56, 61)( 57, 60)
( 58, 59)( 71, 92)( 72, 91)( 73, 90)( 74, 89)( 75, 88)( 76, 87)( 77, 86)
( 78, 85)( 79, 84)( 80, 83)( 81, 82)( 94,115)( 95,114)( 96,113)( 97,112)
( 98,111)( 99,110)(100,109)(101,108)(102,107)(103,106)(104,105)(117,138)
(118,137)(119,136)(120,135)(121,134)(122,133)(123,132)(124,131)(125,130)
(126,129)(127,128)(140,161)(141,160)(142,159)(143,158)(144,157)(145,156)
(146,155)(147,154)(148,153)(149,152)(150,151)(163,184)(164,183)(165,182)
(166,181)(167,180)(168,179)(169,178)(170,177)(171,176)(172,175)(173,174)
(186,207)(187,206)(188,205)(189,204)(190,203)(191,202)(192,201)(193,200)
(194,199)(195,198)(196,197)(209,230)(210,229)(211,228)(212,227)(213,226)
(214,225)(215,224)(216,223)(217,222)(218,221)(219,220);;
s1 := (  1,  2)(  3, 23)(  4, 22)(  5, 21)(  6, 20)(  7, 19)(  8, 18)(  9, 17)
( 10, 16)( 11, 15)( 12, 14)( 24, 94)( 25, 93)( 26,115)( 27,114)( 28,113)
( 29,112)( 30,111)( 31,110)( 32,109)( 33,108)( 34,107)( 35,106)( 36,105)
( 37,104)( 38,103)( 39,102)( 40,101)( 41,100)( 42, 99)( 43, 98)( 44, 97)
( 45, 96)( 46, 95)( 47, 71)( 48, 70)( 49, 92)( 50, 91)( 51, 90)( 52, 89)
( 53, 88)( 54, 87)( 55, 86)( 56, 85)( 57, 84)( 58, 83)( 59, 82)( 60, 81)
( 61, 80)( 62, 79)( 63, 78)( 64, 77)( 65, 76)( 66, 75)( 67, 74)( 68, 73)
( 69, 72)(116,117)(118,138)(119,137)(120,136)(121,135)(122,134)(123,133)
(124,132)(125,131)(126,130)(127,129)(139,209)(140,208)(141,230)(142,229)
(143,228)(144,227)(145,226)(146,225)(147,224)(148,223)(149,222)(150,221)
(151,220)(152,219)(153,218)(154,217)(155,216)(156,215)(157,214)(158,213)
(159,212)(160,211)(161,210)(162,186)(163,185)(164,207)(165,206)(166,205)
(167,204)(168,203)(169,202)(170,201)(171,200)(172,199)(173,198)(174,197)
(175,196)(176,195)(177,194)(178,193)(179,192)(180,191)(181,190)(182,189)
(183,188)(184,187);;
s2 := (  1,139)(  2,140)(  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)( 24,116)
( 25,117)( 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)( 47,208)( 48,209)
( 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)( 70,185)( 71,186)( 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)( 93,162)( 94,163)( 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);;
s3 := (231,232);;
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*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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(232)!(  2, 23)(  3, 22)(  4, 21)(  5, 20)(  6, 19)(  7, 18)(  8, 17)
(  9, 16)( 10, 15)( 11, 14)( 12, 13)( 25, 46)( 26, 45)( 27, 44)( 28, 43)
( 29, 42)( 30, 41)( 31, 40)( 32, 39)( 33, 38)( 34, 37)( 35, 36)( 48, 69)
( 49, 68)( 50, 67)( 51, 66)( 52, 65)( 53, 64)( 54, 63)( 55, 62)( 56, 61)
( 57, 60)( 58, 59)( 71, 92)( 72, 91)( 73, 90)( 74, 89)( 75, 88)( 76, 87)
( 77, 86)( 78, 85)( 79, 84)( 80, 83)( 81, 82)( 94,115)( 95,114)( 96,113)
( 97,112)( 98,111)( 99,110)(100,109)(101,108)(102,107)(103,106)(104,105)
(117,138)(118,137)(119,136)(120,135)(121,134)(122,133)(123,132)(124,131)
(125,130)(126,129)(127,128)(140,161)(141,160)(142,159)(143,158)(144,157)
(145,156)(146,155)(147,154)(148,153)(149,152)(150,151)(163,184)(164,183)
(165,182)(166,181)(167,180)(168,179)(169,178)(170,177)(171,176)(172,175)
(173,174)(186,207)(187,206)(188,205)(189,204)(190,203)(191,202)(192,201)
(193,200)(194,199)(195,198)(196,197)(209,230)(210,229)(211,228)(212,227)
(213,226)(214,225)(215,224)(216,223)(217,222)(218,221)(219,220);
s1 := Sym(232)!(  1,  2)(  3, 23)(  4, 22)(  5, 21)(  6, 20)(  7, 19)(  8, 18)
(  9, 17)( 10, 16)( 11, 15)( 12, 14)( 24, 94)( 25, 93)( 26,115)( 27,114)
( 28,113)( 29,112)( 30,111)( 31,110)( 32,109)( 33,108)( 34,107)( 35,106)
( 36,105)( 37,104)( 38,103)( 39,102)( 40,101)( 41,100)( 42, 99)( 43, 98)
( 44, 97)( 45, 96)( 46, 95)( 47, 71)( 48, 70)( 49, 92)( 50, 91)( 51, 90)
( 52, 89)( 53, 88)( 54, 87)( 55, 86)( 56, 85)( 57, 84)( 58, 83)( 59, 82)
( 60, 81)( 61, 80)( 62, 79)( 63, 78)( 64, 77)( 65, 76)( 66, 75)( 67, 74)
( 68, 73)( 69, 72)(116,117)(118,138)(119,137)(120,136)(121,135)(122,134)
(123,133)(124,132)(125,131)(126,130)(127,129)(139,209)(140,208)(141,230)
(142,229)(143,228)(144,227)(145,226)(146,225)(147,224)(148,223)(149,222)
(150,221)(151,220)(152,219)(153,218)(154,217)(155,216)(156,215)(157,214)
(158,213)(159,212)(160,211)(161,210)(162,186)(163,185)(164,207)(165,206)
(166,205)(167,204)(168,203)(169,202)(170,201)(171,200)(172,199)(173,198)
(174,197)(175,196)(176,195)(177,194)(178,193)(179,192)(180,191)(181,190)
(182,189)(183,188)(184,187);
s2 := Sym(232)!(  1,139)(  2,140)(  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)
( 24,116)( 25,117)( 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)( 47,208)
( 48,209)( 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)( 70,185)( 71,186)
( 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)( 93,162)( 94,163)( 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);
s3 := Sym(232)!(231,232);
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*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

to this polytope