On the boundary of self affine tilings generated by Pisot numbers

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Parry expansions of polynomial sequences. (2002, unknown): “Akiyama [2] obtained tilings of Rd−1 for Pisot units α satisfying the condition Z[α−1] ∩ R ⊂ Fin(α)− Fin(α) ∩ [0, ε) for all ε > 0, (W)”
On the Pisot Substitution Conjecture (2015, background): “For more on these constructions, see [1, 3, 5, 58].”
Atomic surfaces, tilings and coincidence I. irreducible case (2006, methodology): “We will also show there that for fl-substitution, the super-coincidence condition is equivalent to a (W)-property introduced by Akiyama [ Ak2 ].”
A CERTAIN FINITENESS PROPERTY OF PISOT NUMBER SYSTEMS (2004, background): “The first author [3] also showed that the origin is an ‘exclusive’ inner point of the central tile if and only if (F) holds.”
Topological Properties of Rauzy Fractals (2010, background): “This type of graph first appeared in more specific settings in [7, 110, 119].”
Boundary of central tiles associated with Pisot beta-numeration and purely periodic expansions (2007, background): “D S] 1 8 O ct 2 00 7”
A Survey on Topological Properties of Tiles Related to Number Systems (2004, unknown): “p := p + 1 A[p] := Red(A[p− 1]⊗ A[1]) until A[p] = A[p− 1] G(S) := A[p] \ {0}”
Tilings associated with beta-numeration and substitutions. (2005, methodology): “According to [ Aki02 ], we introduce the (countable) set Frac(β) ⊂ X r β defined as the set of β-expansions of real numbers in”