Polytope of Type {8,30}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,30}*1920b
if this polytope has a name.
Group : SmallGroup(1920,237638)
Rank : 3
Schlafli Type : {8,30}
Number of vertices, edges, etc : 32, 480, 120
Order of s0s1s2 : 30
Order of s0s1s2s1 : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-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 : {4,30}*960a
   5-fold quotients : {8,6}*384b
   8-fold quotients : {4,30}*240b
   10-fold quotients : {4,6}*192a
   16-fold quotients : {4,15}*120
   40-fold quotients : {4,6}*48c
   80-fold quotients : {4,3}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<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> of order 2.
      60 facets:
         60 of {8}*16
      20 vertex figures:
         8 of {15}*30
         12 of {30}*60
   P/N, where N=<s0*s2*s1*s0*s2*s1*s0*s1*s2*s1*s2> of order 2.
      60 facets:
         60 of {8}*16
      16 vertex figures:
         16 of {30}*60
   P/N, where N=<s0*s1*s0*s2*s1*s0*s1*s2*s1, s1*s0*s1*s0*s2*s1*s0*s1*s2> of order 4.
      30 facets:
         30 of {8}*16
      8 vertex figures:
         8 of {30}*60
   P/N, where N=<s0*s2*s1*s2*s1*s0*s1*s0*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> of order 4.
      30 facets:
         30 of {8}*16
      12 vertex figures:
         8 of {15}*30
         4 of {30}*60

Permutation Representation (GAP) : 
s0 := (  1, 17)(  2, 18)(  3, 20)(  4, 19)(  5, 21)(  6, 22)(  7, 24)(  8, 23)(  9, 25)( 10, 26)( 11, 28)( 12, 27)( 13, 29)( 14, 30)( 15, 32)( 16, 31)( 33, 49)( 34, 50)( 35, 52)( 36, 51)( 37, 53)( 38, 54)( 39, 56)( 40, 55)( 41, 57)( 42, 58)( 43, 60)( 44, 59)( 45, 61)( 46, 62)( 47, 64)( 48, 63)( 65, 81)( 66, 82)( 67, 84)( 68, 83)( 69, 85)( 70, 86)( 71, 88)( 72, 87)( 73, 89)( 74, 90)( 75, 92)( 76, 91)( 77, 93)( 78, 94)( 79, 96)( 80, 95)( 97,113)( 98,114)( 99,116)(100,115)(101,117)(102,118)(103,120)(104,119)(105,121)(106,122)(107,124)(108,123)(109,125)(110,126)(111,128)(112,127)(129,145)(130,146)(131,148)(132,147)(133,149)(134,150)(135,152)(136,151)(137,153)(138,154)(139,156)(140,155)(141,157)(142,158)(143,160)(144,159);;
s1 := (  5,  7)(  6,  8)(  9, 12)( 10, 11)( 13, 14)( 15, 16)( 17, 32)( 18, 31)( 19, 30)( 20, 29)( 21, 26)( 22, 25)( 23, 28)( 24, 27)( 33,129)( 34,130)( 35,131)( 36,132)( 37,135)( 38,136)( 39,133)( 40,134)( 41,140)( 42,139)( 43,138)( 44,137)( 45,142)( 46,141)( 47,144)( 48,143)( 49,160)( 50,159)( 51,158)( 52,157)( 53,154)( 54,153)( 55,156)( 56,155)( 57,150)( 58,149)( 59,152)( 60,151)( 61,148)( 62,147)( 63,146)( 64,145)( 65, 97)( 66, 98)( 67, 99)( 68,100)( 69,103)( 70,104)( 71,101)( 72,102)( 73,108)( 74,107)( 75,106)( 76,105)( 77,110)( 78,109)( 79,112)( 80,111)( 81,128)( 82,127)( 83,126)( 84,125)( 85,122)( 86,121)( 87,124)( 88,123)( 89,118)( 90,117)( 91,120)( 92,119)( 93,116)( 94,115)( 95,114)( 96,113);;
s2 := (  1, 33)(  2, 34)(  3, 39)(  4, 40)(  5, 37)(  6, 38)(  7, 35)(  8, 36)(  9, 57)( 10, 58)( 11, 63)( 12, 64)( 13, 61)( 14, 62)( 15, 59)( 16, 60)( 17, 49)( 18, 50)( 19, 55)( 20, 56)( 21, 53)( 22, 54)( 23, 51)( 24, 52)( 25, 41)( 26, 42)( 27, 47)( 28, 48)( 29, 45)( 30, 46)( 31, 43)( 32, 44)( 65,129)( 66,130)( 67,135)( 68,136)( 69,133)( 70,134)( 71,131)( 72,132)( 73,153)( 74,154)( 75,159)( 76,160)( 77,157)( 78,158)( 79,155)( 80,156)( 81,145)( 82,146)( 83,151)( 84,152)( 85,149)( 86,150)( 87,147)( 88,148)( 89,137)( 90,138)( 91,143)( 92,144)( 93,141)( 94,142)( 95,139)( 96,140)( 99,103)(100,104)(105,121)(106,122)(107,127)(108,128)(109,125)(110,126)(111,123)(112,124)(115,119)(116,120);;
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*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, 
s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*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 ];;
poly := F / rels;;
Permutation Representation (Magma) : 
s0 := Sym(160)!(  1, 17)(  2, 18)(  3, 20)(  4, 19)(  5, 21)(  6, 22)(  7, 24)(  8, 23)(  9, 25)( 10, 26)( 11, 28)( 12, 27)( 13, 29)( 14, 30)( 15, 32)( 16, 31)( 33, 49)( 34, 50)( 35, 52)( 36, 51)( 37, 53)( 38, 54)( 39, 56)( 40, 55)( 41, 57)( 42, 58)( 43, 60)( 44, 59)( 45, 61)( 46, 62)( 47, 64)( 48, 63)( 65, 81)( 66, 82)( 67, 84)( 68, 83)( 69, 85)( 70, 86)( 71, 88)( 72, 87)( 73, 89)( 74, 90)( 75, 92)( 76, 91)( 77, 93)( 78, 94)( 79, 96)( 80, 95)( 97,113)( 98,114)( 99,116)(100,115)(101,117)(102,118)(103,120)(104,119)(105,121)(106,122)(107,124)(108,123)(109,125)(110,126)(111,128)(112,127)(129,145)(130,146)(131,148)(132,147)(133,149)(134,150)(135,152)(136,151)(137,153)(138,154)(139,156)(140,155)(141,157)(142,158)(143,160)(144,159);
s1 := Sym(160)!(  5,  7)(  6,  8)(  9, 12)( 10, 11)( 13, 14)( 15, 16)( 17, 32)( 18, 31)( 19, 30)( 20, 29)( 21, 26)( 22, 25)( 23, 28)( 24, 27)( 33,129)( 34,130)( 35,131)( 36,132)( 37,135)( 38,136)( 39,133)( 40,134)( 41,140)( 42,139)( 43,138)( 44,137)( 45,142)( 46,141)( 47,144)( 48,143)( 49,160)( 50,159)( 51,158)( 52,157)( 53,154)( 54,153)( 55,156)( 56,155)( 57,150)( 58,149)( 59,152)( 60,151)( 61,148)( 62,147)( 63,146)( 64,145)( 65, 97)( 66, 98)( 67, 99)( 68,100)( 69,103)( 70,104)( 71,101)( 72,102)( 73,108)( 74,107)( 75,106)( 76,105)( 77,110)( 78,109)( 79,112)( 80,111)( 81,128)( 82,127)( 83,126)( 84,125)( 85,122)( 86,121)( 87,124)( 88,123)( 89,118)( 90,117)( 91,120)( 92,119)( 93,116)( 94,115)( 95,114)( 96,113);
s2 := Sym(160)!(  1, 33)(  2, 34)(  3, 39)(  4, 40)(  5, 37)(  6, 38)(  7, 35)(  8, 36)(  9, 57)( 10, 58)( 11, 63)( 12, 64)( 13, 61)( 14, 62)( 15, 59)( 16, 60)( 17, 49)( 18, 50)( 19, 55)( 20, 56)( 21, 53)( 22, 54)( 23, 51)( 24, 52)( 25, 41)( 26, 42)( 27, 47)( 28, 48)( 29, 45)( 30, 46)( 31, 43)( 32, 44)( 65,129)( 66,130)( 67,135)( 68,136)( 69,133)( 70,134)( 71,131)( 72,132)( 73,153)( 74,154)( 75,159)( 76,160)( 77,157)( 78,158)( 79,155)( 80,156)( 81,145)( 82,146)( 83,151)( 84,152)( 85,149)( 86,150)( 87,147)( 88,148)( 89,137)( 90,138)( 91,143)( 92,144)( 93,141)( 94,142)( 95,139)( 96,140)( 99,103)(100,104)(105,121)(106,122)(107,127)(108,128)(109,125)(110,126)(111,123)(112,124)(115,119)(116,120);
poly := sub<Sym(160)|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*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, 
s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*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 >;
References : None.
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