Polytope of Type {30,8}

Play with this polytope as a twisty puzzle

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

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