Polytope of Type {8,38}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,38}*608
Also Known As : {8,38|2}. if this polytope has another name.
Group : SmallGroup(608,105)
Rank : 3
Schlafli Type : {8,38}
Number of vertices, edges, etc : 8, 152, 38
Order of s0s1s2 : 152
Order of s0s1s2s1 : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {8,38,2} of size 1216
Vertex Figure Of :
   {2,8,38} of size 1216
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,38}*304
   4-fold quotients : {2,38}*152
   8-fold quotients : {2,19}*76
   19-fold quotients : {8,2}*32
   38-fold quotients : {4,2}*16
   76-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {8,76}*1216a, {16,38}*1216
   3-fold covers : {24,38}*1824, {8,114}*1824
Irregular Quotients (of which this is a minimal cover):
   None.

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