Polytope of Type {8,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,4}*1600a
if this polytope has a name.
Group : SmallGroup(1600,6672)
Rank : 3
Schlafli Type : {8,4}
Number of vertices, edges, etc : 200, 400, 100
Order of s₀s₁s₂ : 40
Order of s₀s₁s₂s₁ : 10
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
   Skewing Operation
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}*64a
   50-fold quotients : {4,4}*32, {8,2}*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 := (  1,101)(  2,112)(  3,123)(  4,109)(  5,120)(  6,121)(  7,107)(  8,118)
(  9,104)( 10,115)( 11,116)( 12,102)( 13,113)( 14,124)( 15,110)( 16,111)
( 17,122)( 18,108)( 19,119)( 20,105)( 21,106)( 22,117)( 23,103)( 24,114)
( 25,125)( 26,126)( 27,137)( 28,148)( 29,134)( 30,145)( 31,146)( 32,132)
( 33,143)( 34,129)( 35,140)( 36,141)( 37,127)( 38,138)( 39,149)( 40,135)
( 41,136)( 42,147)( 43,133)( 44,144)( 45,130)( 46,131)( 47,142)( 48,128)
( 49,139)( 50,150)( 51,176)( 52,187)( 53,198)( 54,184)( 55,195)( 56,196)
( 57,182)( 58,193)( 59,179)( 60,190)( 61,191)( 62,177)( 63,188)( 64,199)
( 65,185)( 66,186)( 67,197)( 68,183)( 69,194)( 70,180)( 71,181)( 72,192)
( 73,178)( 74,189)( 75,200)( 76,151)( 77,162)( 78,173)( 79,159)( 80,170)
( 81,171)( 82,157)( 83,168)( 84,154)( 85,165)( 86,166)( 87,152)( 88,163)
( 89,174)( 90,160)( 91,161)( 92,172)( 93,158)( 94,169)( 95,155)( 96,156)
( 97,167)( 98,153)( 99,164)(100,175);;
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,  7)(  2, 21)(  3, 15)(  5, 18)(  6, 12)(  8, 20)( 10, 23)( 11, 17)
( 13, 25)( 16, 22)( 26, 32)( 27, 46)( 28, 40)( 30, 43)( 31, 37)( 33, 45)
( 35, 48)( 36, 42)( 38, 50)( 41, 47)( 51, 57)( 52, 71)( 53, 65)( 55, 68)
( 56, 62)( 58, 70)( 60, 73)( 61, 67)( 63, 75)( 66, 72)( 76, 82)( 77, 96)
( 78, 90)( 80, 93)( 81, 87)( 83, 95)( 85, 98)( 86, 92)( 88,100)( 91, 97)
(101,107)(102,121)(103,115)(105,118)(106,112)(108,120)(110,123)(111,117)
(113,125)(116,122)(126,132)(127,146)(128,140)(130,143)(131,137)(133,145)
(135,148)(136,142)(138,150)(141,147)(151,157)(152,171)(153,165)(155,168)
(156,162)(158,170)(160,173)(161,167)(163,175)(166,172)(176,182)(177,196)
(178,190)(180,193)(181,187)(183,195)(185,198)(186,192)(188,200)(191,197);;
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, 
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*s2*s1*s0*s1*s2*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

References : None.
to this polytope