Polytope of Type {4,8}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,8}*1600a
if this polytope has a name.
Group : SmallGroup(1600,6672)
Rank : 3
Schlafli Type : {4,8}
Number of vertices, edges, etc : 100, 400, 200
Order of s0s1s2 : 40
Order of s0s1s2s1 : 10
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
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 : {4,4}*800
   4-fold quotients : {4,4}*400
   8-fold quotients : {4,4}*200
   25-fold quotients : {4,8}*64a
   50-fold quotients : {4,4}*32, {2,8}*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=<s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2> of order 2.
      100 facets:
         100 of {4}*8
      50 vertex figures:
         50 of {8}*16
   P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2> of order 2.
      100 facets:
         100 of {4}*8
      50 vertex figures:
         50 of {8}*16
   P/N, where N=<s0*s1*s0*s1> of order 2.
      104 facets:
         8 of {2}*4
         96 of {4}*8
      50 vertex figures:
         50 of {8}*16
   P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1> of order 5.
      40 facets:
         40 of {4}*8
      20 vertex figures:
         20 of {8}*16
   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.
      40 facets:
         40 of {4}*8
      20 vertex figures:
         20 of {8}*16
   P/N, where N=<s0*s1*s2*s1*s0*s2*s1*s0*s1*s2*s1*s0*s2*s1> of order 5.
      40 facets:
         40 of {4}*8
      20 vertex figures:
         20 of {8}*16
   P/N, where N=<s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1> of order 10.
      24 facets:
         8 of {2}*4
         16 of {4}*8
      10 vertex figures:
         10 of {8}*16
   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 10.
      24 facets:
         8 of {2}*4
         16 of {4}*8
      10 vertex figures:
         10 of {8}*16
   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.
      20 facets:
         20 of {4}*8
      10 vertex figures:
         10 of {8}*16
   P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1, s0*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2> of order 10.
      20 facets:
         20 of {4}*8
      10 vertex figures:
         10 of {8}*16
   P/N, where N=<s0*s2*s1*s0*s2*s1*s0*s1*s2*s1> of order 10.
      20 facets:
         20 of {4}*8
      10 vertex figures:
         10 of {8}*16
   P/N, where N=<s0*s1*s0*s1, s0*s2*s1*s0*s2*s1*s0*s1*s2*s1*s0*s2> of order 10.
      24 facets:
         8 of {2}*4
         16 of {4}*8
      10 vertex figures:
         10 of {8}*16
   P/N, where N=<s0*s1*s2*s1*s0*s2*s1*s0*s1*s2*s1*s0*s2*s1, s0*s1*s0*s2*s1*s0*s2*s1*s0*s1*s2*s1*s0*s2*s1*s2> of order 10.
      20 facets:
         20 of {4}*8
      10 vertex figures:
         10 of {8}*16

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