Polytope of Type {8,50}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,50}*800
Also Known As : {8,50|2}. if this polytope has another name.
Group : SmallGroup(800,131)
Rank : 3
Schlafli Type : {8,50}
Number of vertices, edges, etc : 8, 200, 50
Order of s₀s₁s₂ : 200
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {8,50,2} of size 1600
Vertex Figure Of :
   {2,8,50} of size 1600
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,50}*400
   4-fold quotients : {2,50}*200
   5-fold quotients : {8,10}*160
   8-fold quotients : {2,25}*100
   10-fold quotients : {4,10}*80
   20-fold quotients : {2,10}*40
   25-fold quotients : {8,2}*32
   40-fold quotients : {2,5}*20
   50-fold quotients : {4,2}*16
   100-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {8,100}*1600a, {16,50}*1600
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope