Polytope of Type {36,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {36,8}*1152b
if this polytope has a name.
Group : SmallGroup(1152,32535)
Rank : 3
Schlafli Type : {36,8}
Number of vertices, edges, etc : 72, 288, 16
Order of s₀s₁s₂ : 36
Order of s₀s₁s₂s₁ : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   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 : {36,4}*576a
   3-fold quotients : {12,8}*384b
   4-fold quotients : {36,4}*288a
   6-fold quotients : {12,4}*192a
   8-fold quotients : {36,2}*144, {18,4}*144a
   9-fold quotients : {4,8}*128b
   12-fold quotients : {12,4}*96a
   16-fold quotients : {18,2}*72
   18-fold quotients : {4,4}*64
   24-fold quotients : {12,2}*48, {6,4}*48a
   32-fold quotients : {9,2}*36
   36-fold quotients : {4,4}*32
   48-fold quotients : {6,2}*24
   72-fold quotients : {2,4}*16, {4,2}*16
   96-fold quotients : {3,2}*12
   144-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  2,  3)(  4,  9)(  5,  8)(  6,  7)( 11, 12)( 13, 18)( 14, 17)( 15, 16)
( 20, 21)( 22, 27)( 23, 26)( 24, 25)( 29, 30)( 31, 36)( 32, 35)( 33, 34)
( 37, 64)( 38, 66)( 39, 65)( 40, 72)( 41, 71)( 42, 70)( 43, 69)( 44, 68)
( 45, 67)( 46, 55)( 47, 57)( 48, 56)( 49, 63)( 50, 62)( 51, 61)( 52, 60)
( 53, 59)( 54, 58)( 74, 75)( 76, 81)( 77, 80)( 78, 79)( 83, 84)( 85, 90)
( 86, 89)( 87, 88)( 92, 93)( 94, 99)( 95, 98)( 96, 97)(101,102)(103,108)
(104,107)(105,106)(109,136)(110,138)(111,137)(112,144)(113,143)(114,142)
(115,141)(116,140)(117,139)(118,127)(119,129)(120,128)(121,135)(122,134)
(123,133)(124,132)(125,131)(126,130);;
s1 := (  1,  4)(  2,  6)(  3,  5)(  7,  9)( 10, 13)( 11, 15)( 12, 14)( 16, 18)
( 19, 31)( 20, 33)( 21, 32)( 22, 28)( 23, 30)( 24, 29)( 25, 36)( 26, 35)
( 27, 34)( 37, 40)( 38, 42)( 39, 41)( 43, 45)( 46, 49)( 47, 51)( 48, 50)
( 52, 54)( 55, 67)( 56, 69)( 57, 68)( 58, 64)( 59, 66)( 60, 65)( 61, 72)
( 62, 71)( 63, 70)( 73,112)( 74,114)( 75,113)( 76,109)( 77,111)( 78,110)
( 79,117)( 80,116)( 81,115)( 82,121)( 83,123)( 84,122)( 85,118)( 86,120)
( 87,119)( 88,126)( 89,125)( 90,124)( 91,139)( 92,141)( 93,140)( 94,136)
( 95,138)( 96,137)( 97,144)( 98,143)( 99,142)(100,130)(101,132)(102,131)
(103,127)(104,129)(105,128)(106,135)(107,134)(108,133);;
s2 := (  1, 73)(  2, 74)(  3, 75)(  4, 76)(  5, 77)(  6, 78)(  7, 79)(  8, 80)
(  9, 81)( 10, 82)( 11, 83)( 12, 84)( 13, 85)( 14, 86)( 15, 87)( 16, 88)
( 17, 89)( 18, 90)( 19, 91)( 20, 92)( 21, 93)( 22, 94)( 23, 95)( 24, 96)
( 25, 97)( 26, 98)( 27, 99)( 28,100)( 29,101)( 30,102)( 31,103)( 32,104)
( 33,105)( 34,106)( 35,107)( 36,108)( 37,136)( 38,137)( 39,138)( 40,139)
( 41,140)( 42,141)( 43,142)( 44,143)( 45,144)( 46,127)( 47,128)( 48,129)
( 49,130)( 50,131)( 51,132)( 52,133)( 53,134)( 54,135)( 55,118)( 56,119)
( 57,120)( 58,121)( 59,122)( 60,123)( 61,124)( 62,125)( 63,126)( 64,109)
( 65,110)( 66,111)( 67,112)( 68,113)( 69,114)( 70,115)( 71,116)( 72,117);;
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*s2*s0*s1*s2*s0*s1*s2*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(144)!(  2,  3)(  4,  9)(  5,  8)(  6,  7)( 11, 12)( 13, 18)( 14, 17)
( 15, 16)( 20, 21)( 22, 27)( 23, 26)( 24, 25)( 29, 30)( 31, 36)( 32, 35)
( 33, 34)( 37, 64)( 38, 66)( 39, 65)( 40, 72)( 41, 71)( 42, 70)( 43, 69)
( 44, 68)( 45, 67)( 46, 55)( 47, 57)( 48, 56)( 49, 63)( 50, 62)( 51, 61)
( 52, 60)( 53, 59)( 54, 58)( 74, 75)( 76, 81)( 77, 80)( 78, 79)( 83, 84)
( 85, 90)( 86, 89)( 87, 88)( 92, 93)( 94, 99)( 95, 98)( 96, 97)(101,102)
(103,108)(104,107)(105,106)(109,136)(110,138)(111,137)(112,144)(113,143)
(114,142)(115,141)(116,140)(117,139)(118,127)(119,129)(120,128)(121,135)
(122,134)(123,133)(124,132)(125,131)(126,130);
s1 := Sym(144)!(  1,  4)(  2,  6)(  3,  5)(  7,  9)( 10, 13)( 11, 15)( 12, 14)
( 16, 18)( 19, 31)( 20, 33)( 21, 32)( 22, 28)( 23, 30)( 24, 29)( 25, 36)
( 26, 35)( 27, 34)( 37, 40)( 38, 42)( 39, 41)( 43, 45)( 46, 49)( 47, 51)
( 48, 50)( 52, 54)( 55, 67)( 56, 69)( 57, 68)( 58, 64)( 59, 66)( 60, 65)
( 61, 72)( 62, 71)( 63, 70)( 73,112)( 74,114)( 75,113)( 76,109)( 77,111)
( 78,110)( 79,117)( 80,116)( 81,115)( 82,121)( 83,123)( 84,122)( 85,118)
( 86,120)( 87,119)( 88,126)( 89,125)( 90,124)( 91,139)( 92,141)( 93,140)
( 94,136)( 95,138)( 96,137)( 97,144)( 98,143)( 99,142)(100,130)(101,132)
(102,131)(103,127)(104,129)(105,128)(106,135)(107,134)(108,133);
s2 := Sym(144)!(  1, 73)(  2, 74)(  3, 75)(  4, 76)(  5, 77)(  6, 78)(  7, 79)
(  8, 80)(  9, 81)( 10, 82)( 11, 83)( 12, 84)( 13, 85)( 14, 86)( 15, 87)
( 16, 88)( 17, 89)( 18, 90)( 19, 91)( 20, 92)( 21, 93)( 22, 94)( 23, 95)
( 24, 96)( 25, 97)( 26, 98)( 27, 99)( 28,100)( 29,101)( 30,102)( 31,103)
( 32,104)( 33,105)( 34,106)( 35,107)( 36,108)( 37,136)( 38,137)( 39,138)
( 40,139)( 41,140)( 42,141)( 43,142)( 44,143)( 45,144)( 46,127)( 47,128)
( 48,129)( 49,130)( 50,131)( 51,132)( 52,133)( 53,134)( 54,135)( 55,118)
( 56,119)( 57,120)( 58,121)( 59,122)( 60,123)( 61,124)( 62,125)( 63,126)
( 64,109)( 65,110)( 66,111)( 67,112)( 68,113)( 69,114)( 70,115)( 71,116)
( 72,117);
poly := sub<Sym(144)|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*s2*s0*s1*s2*s0*s1*s2*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

References : None.
to this polytope