Polytope of Type {8,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,4}*1600b
if this polytope has a name.
Group : SmallGroup(1600,6690)
Rank : 3
Schlafli Type : {8,4}
Number of vertices, edges, etc : 200, 400, 100
Order of s₀s₁s₂ : 40
Order of s₀s₁s₂s₁ : 20
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,4}*800
   4-fold quotients : {4,4}*400
   8-fold quotients : {4,4}*200
   25-fold quotients : {8,4}*64b
   50-fold quotients : {4,4}*32
   100-fold quotients : {2,4}*16, {4,2}*16
   200-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope