Polytope of Type {8,4}

Play with this polytope as a twisty puzzle

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.
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1> of order 2.
      50 facets:
         50 of {8}*16
      100 vertex figures:
         100 of {4}*8
   P/N, where N=<s0*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s2> of order 2.
      50 facets:
         50 of {8}*16
      100 vertex figures:
         100 of {4}*8
   P/N, where N=<s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s2> of order 2.
      50 facets:
         50 of {8}*16
      104 vertex figures:
         96 of {4}*8
         8 of {2}*4
   P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1> of order 5.
      20 facets:
         20 of {8}*16
      40 vertex figures:
         40 of {4}*8
   P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*s1*s2*s1*s0*s2*s1*s2> of order 5.
      20 facets:
         20 of {8}*16
      40 vertex figures:
         40 of {4}*8
   P/N, where N=<s0*s1*s2*s1*s0*s2*s1*s0*s1*s2*s1*s0*s2*s1> of order 5.
      20 facets:
         20 of {8}*16
      40 vertex figures:
         40 of {4}*8
   P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1, s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s2*s1*s2> of order 10.
      10 facets:
         10 of {8}*16
      24 vertex figures:
         16 of {4}*8
         8 of {2}*4
   P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1, s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s2*s1*s2> of order 10.
      10 facets:
         10 of {8}*16
      20 vertex figures:
         20 of {4}*8
   P/N, where N=<s0*s2*s1*s0*s1*s2*s1*s0*s2*s1*s0*s2, s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s2> of order 10.
      10 facets:
         10 of {8}*16
      24 vertex figures:
         16 of {4}*8
         8 of {2}*4
   P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1, s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2> of order 10.
      10 facets:
         10 of {8}*16
      20 vertex figures:
         20 of {4}*8
   P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s2*s1*s2> of order 10.
      10 facets:
         10 of {8}*16
      20 vertex figures:
         20 of {4}*8
   P/N, where N=<s0*s1*s2*s1*s0*s2, s1*s0*s1*s2*s1*s0*s2*s1> of order 10.
      10 facets:
         10 of {8}*16
      24 vertex figures:
         16 of {4}*8
         8 of {2}*4
   P/N, where N=<s0*s1*s2*s1*s0*s2*s1*s0*s1*s2*s1*s0*s2*s1, s0*s1*s0*s2*s1*s0*s1*s2*s1*s0*s2*s1*s0*s2*s1*s2> of order 10.
      10 facets:
         10 of {8}*16
      20 vertex figures:
         20 of {4}*8

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*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*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*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*s0*s1*s2*s1 >;
References : None.
to this polytope

Twisty Puzzle