Polytope of Type {50,4,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {50,4,4}*1600
Also Known As : {{50,4|2},{4,4|2}}. if this polytope has another name.
Group : SmallGroup(1600,1264)
Rank : 4
Schlafli Type : {50,4,4}
Number of vertices, edges, etc : 50, 100, 8, 4
Order of s₀s₁s₂s₃ : 100
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   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) :
   2-fold quotients : {50,2,4}*800, {50,4,2}*800
   4-fold quotients : {25,2,4}*400, {50,2,2}*400
   5-fold quotients : {10,4,4}*320
   8-fold quotients : {25,2,2}*200
   10-fold quotients : {10,2,4}*160, {10,4,2}*160
   20-fold quotients : {5,2,4}*80, {10,2,2}*80
   25-fold quotients : {2,4,4}*64
   40-fold quotients : {5,2,2}*40
   50-fold quotients : {2,2,4}*32, {2,4,2}*32
   100-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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