Polytope of Type {8,36}

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

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

Permutation Representation (Magma) :

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

References : None.
to this polytope