Dual polytopes and tessellations Dual polyhedron

the square tiling, {4,4}, self-dual, shown these red , blue tilings



the infinite-order apeirogonal tiling, {∞,∞} in red, , dual position in blue

the primary class of self-dual polytopes regular polytopes palindromic schläfli symbols. regular polygons, {a} self-dual, polyhedra of form {a,a}, 4-polytopes of form {a,b,a}, 5-polytopes of form {a,b,b,a}, etc.

the self-dual regular polytopes are:

all regular polygons, {a}.
regular tetrahedron: {3,3}
in general, regular n-simplexes, {3,3,...,3}
the regular 24-cell in 4 dimensions, {3,4,3}.
the great 120-cell {5,5/2,5} , grand stellated 120-cell {5/2,5,5/2}

the self-dual (infinite) regular euclidean honeycombs are:

apeirogon: {∞}
square tiling: {4,4}
cubic honeycomb: {4,3,4}
in general, regular n-dimensional euclidean hypercubic honeycombs: {4,3,...,3,4}.

the self-dual (infinite) regular hyperbolic honeycombs are:

compact hyperbolic tilings: {5,5}, {6,6}, ... {p,p}.
paracompact hyperbolic tiling: {∞,∞}
compact hyperbolic honeycombs: {3,5,3}, {5,3,5}, , {5,3,3,5}
paracompact hyperbolic honeycombs: {3,6,3}, {6,3,6}, {4,4,4}, , {3,3,4,3,3}