Polytope of Type {24,4}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24,4}*192d
if this polytope has a name.
Group : SmallGroup(192,961)
Rank : 3
Schlafli Type : {24,4}
Number of vertices, edges, etc : 24, 48, 4
Order of s₀s₁s₂ : 24
Order of s₀s₁s₂s₁ : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
   Flat
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
   Skewing Operation
Facet Of :
   {24,4,2} of size 384
Vertex Figure Of :
   {2,24,4} of size 384
   {4,24,4} of size 768
   {4,24,4} of size 768
   {4,24,4} of size 768
   {4,24,4} of size 768
   {6,24,4} of size 1152
   {6,24,4} of size 1152
   {10,24,4} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {12,4}*96b
   4-fold quotients : {6,4}*48c
   8-fold quotients : {3,4}*24
Covers (Minimal Covers in Boldface) :
   2-fold covers : {24,4}*384c
   3-fold covers : {72,4}*576d
   4-fold covers : {24,4}*768f, {24,8}*768i, {24,8}*768k, {24,4}*768i, {48,4}*768c, {48,4}*768d
   5-fold covers : {120,4}*960d
   6-fold covers : {72,4}*1152c, {24,12}*1152o, {24,12}*1152p
   7-fold covers : {168,4}*1344d
   9-fold covers : {216,4}*1728d
   10-fold covers : {24,20}*1920c, {120,4}*1920c
Irregular Quotients (of which this is a minimal cover):
   None.

Permutation Representation (GAP) :

s0 := ( 2, 3)( 5, 9)( 6,11)( 7,10)( 8,12)(14,15)(17,21)(18,23)(19,22)(20,24)(25,37)(26,39)(27,38)(28,40)(29,45)(30,47)(31,46)(32,48)(33,41)(34,43)(35,42)(36,44)(49,73)(50,75)(51,74)(52,76)(53,81)(54,83)(55,82)(56,84)(57,77)(58,79)(59,78)(60,80)(61,85)(62,87)(63,86)(64,88)(65,93)(66,95)(67,94)(68,96)(69,89)(70,91)(71,90)(72,92);;
s1 := ( 1,53)( 2,54)( 3,56)( 4,55)( 5,49)( 6,50)( 7,52)( 8,51)( 9,57)(10,58)(11,60)(12,59)(13,65)(14,66)(15,68)(16,67)(17,61)(18,62)(19,64)(20,63)(21,69)(22,70)(23,72)(24,71)(25,89)(26,90)(27,92)(28,91)(29,85)(30,86)(31,88)(32,87)(33,93)(34,94)(35,96)(36,95)(37,77)(38,78)(39,80)(40,79)(41,73)(42,74)(43,76)(44,75)(45,81)(46,82)(47,84)(48,83);;
s2 := ( 1,16)( 2,15)( 3,14)( 4,13)( 5,20)( 6,19)( 7,18)( 8,17)( 9,24)(10,23)(11,22)(12,21)(25,40)(26,39)(27,38)(28,37)(29,44)(30,43)(31,42)(32,41)(33,48)(34,47)(35,46)(36,45)(49,64)(50,63)(51,62)(52,61)(53,68)(54,67)(55,66)(56,65)(57,72)(58,71)(59,70)(60,69)(73,88)(74,87)(75,86)(76,85)(77,92)(78,91)(79,90)(80,89)(81,96)(82,95)(83,94)(84,93);;
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, 
s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1, 
s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*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(96)!( 2, 3)( 5, 9)( 6,11)( 7,10)( 8,12)(14,15)(17,21)(18,23)(19,22)(20,24)(25,37)(26,39)(27,38)(28,40)(29,45)(30,47)(31,46)(32,48)(33,41)(34,43)(35,42)(36,44)(49,73)(50,75)(51,74)(52,76)(53,81)(54,83)(55,82)(56,84)(57,77)(58,79)(59,78)(60,80)(61,85)(62,87)(63,86)(64,88)(65,93)(66,95)(67,94)(68,96)(69,89)(70,91)(71,90)(72,92);
s1 := Sym(96)!( 1,53)( 2,54)( 3,56)( 4,55)( 5,49)( 6,50)( 7,52)( 8,51)( 9,57)(10,58)(11,60)(12,59)(13,65)(14,66)(15,68)(16,67)(17,61)(18,62)(19,64)(20,63)(21,69)(22,70)(23,72)(24,71)(25,89)(26,90)(27,92)(28,91)(29,85)(30,86)(31,88)(32,87)(33,93)(34,94)(35,96)(36,95)(37,77)(38,78)(39,80)(40,79)(41,73)(42,74)(43,76)(44,75)(45,81)(46,82)(47,84)(48,83);
s2 := Sym(96)!( 1,16)( 2,15)( 3,14)( 4,13)( 5,20)( 6,19)( 7,18)( 8,17)( 9,24)(10,23)(11,22)(12,21)(25,40)(26,39)(27,38)(28,37)(29,44)(30,43)(31,42)(32,41)(33,48)(34,47)(35,46)(36,45)(49,64)(50,63)(51,62)(52,61)(53,68)(54,67)(55,66)(56,65)(57,72)(58,71)(59,70)(60,69)(73,88)(74,87)(75,86)(76,85)(77,92)(78,91)(79,90)(80,89)(81,96)(82,95)(83,94)(84,93);
poly := sub<Sym(96)|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, 
s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1, 
s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

References : None.
to this polytope

Polytope of Type {24,4}

Twisty Puzzle