Polytope of Type {48,6}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {48,6}*576c
if this polytope has a name.
Group : SmallGroup(576,2907)
Rank : 3
Schlafli Type : {48,6}
Number of vertices, edges, etc : 48, 144, 6
Order of s₀s₁s₂ : 48
Order of s₀s₁s₂s₁ : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {48,6,2} of size 1152
Vertex Figure Of :
   {2,48,6} of size 1152
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {24,6}*288c
   3-fold quotients : {16,6}*192
   4-fold quotients : {12,6}*144c
   6-fold quotients : {8,6}*96
   8-fold quotients : {6,6}*72b
   9-fold quotients : {16,2}*64
   12-fold quotients : {4,6}*48a
   16-fold quotients : {6,3}*36
   18-fold quotients : {8,2}*32
   24-fold quotients : {2,6}*24
   36-fold quotients : {4,2}*16
   48-fold quotients : {2,3}*12
   72-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {48,12}*1152c, {96,6}*1152a
   3-fold covers : {48,18}*1728b, {48,6}*1728c, {48,6}*1728f
Irregular Quotients (of which this is a minimal cover):
   None.

Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope

Polytope of Type {48,6}

Twisty Puzzle