### Table 1: Root mean square errors in percent of edge length of volume cell for reconstructions from subsets of coeffi- cients.

"... In PAGE 8: ... Assuming that the control points of the shrink-wrapped mesh interpolate the isosurface, we can estimate the root mean square error (RMSE) for a mesh reconstructed from only a subset of coefficients by using differences between control points at finest resolution. Error estimates are shown in Table1 . The errors are computed in percent of the edge length of one volume cell.... ..."

### Table 1: Root mean square errors in percent of edge length of volume cell for reconstructions from subsets of coeffi- cients.

"... In PAGE 8: ... Assuming that the control points of the shrink-wrapped mesh interpolate the isosurface, we can estimate the root mean square error (RMSE) for a mesh reconstructed from only a subset of coefficients by using differences between control points at finest resolution. Error estimates are shown in Table1 . The errors are computed in percent of the edge length of one volume cell.... ..."

### Table 1: Root mean square errors in percent of edge length of vol- ume cell for reconstructions from subsets of coefficients.

### Table 1: Cells generated as edge sums in A(0), with inner normals and constraints on the lifting values for the arti cial origins. Their volume and the inner normal of the corresponding cell in S is listed. The last column gives the smallest set I for which the cell is I-stable.

"... In PAGE 8: ...must satisfy 8 gt; lt; gt; : ha; vi = hd; vi : v2 = M1 hf; vi = hg; vi : 2v1 + 1 = 3v1 + v2 and 8 gt; lt; gt; : ha; vi lt; hb; vi : v2 lt; 2v2 + 1 ha; vi lt; hc; vi : v2 lt; v1 + 3v2 hf; vi lt; he; vi : 2v1 + 1 lt; v1 hf; vi lt; hh; vi : 2v1 + 1 lt; M2 : (8) For the solution v = (?M1 +1; M1; 1) of the linear system, the third inequality yields M1 gt; 2. In Table1 , we list the results of the edge-edge combinations and the constraints they... In PAGE 8: ... If the coe cients are generic, the polynomial system is ay + by2 + cxy3 = ex + fx2 + gx3y = 0: (9) The cell volumes correctly compute the generic root counts in all cases. In Table1 we see that cells (ad; fg) and (bc; eh) are not stable for any index set I. There are 3 roots in C 2 0, 2 roots with exactly one zero coordinate, and one root equals 0.... ..."

### Table 1: Cells generated as edge sums in A(0), with inner normals and constraints on the lifting values for the arti cial origins. Their volume and the inner normal of the corresponding cell in S is listed. The last column gives the smallest set I for which the cell is I-stable.

"... In PAGE 7: ... The inner normal v = (v1; v2; 1) must satisfy 8 gt; gt; lt; gt; gt; : ha; vi = hd; vi : v2 = M1 hf; vi = hg; vi : 2v1 + 1 = 3v1 + v2 and 8 gt; gt; lt; gt; gt; : ha; vi lt; hb; vi : v2 lt; 2v2 + 1 ha; vi lt; hc; vi : v2 lt; v1 + 3v2 hf; vi lt; he; vi : 2v1 + 1 lt; v1 hf; vi lt; hh; vi : 2v1 + 1 lt; M2 : (11) For the solution v = (?M1 +1; M1; 1) of the linear system, the third inequality yields M1 gt; 2. In Table1 , we list the results of the edge-edge combinations and the constraints they imply. The considered point con guration corresponds to a pair of polynomials in two variables x; y.... In PAGE 7: ... If the coe cients are generic, the polynomial system is ay + by2 + cxy3 = ex + fx2 + gx3y = 0: (12) The cell volumes correctly compute the generic root counts in all cases. In Table1 we see that cells (ad; fg) and (bc; eh) are not stable for any index set I. There are 3 roots in C 2 0, 2 roots with exactly one zero coordinate, and one root equals 0.... ..."

### Table 1: Cells generated as edge sums in A(0), with inner normals and constraints on the lifting values for the arti cial origins. Their volume and the inner normal of the corresponding cell in S is listed. The last column gives the smallest set I for which the cell is I-stable.

"... In PAGE 11: ... The inner normal v = (v1; v2; 1) must satisfy 8 gt; gt; lt; gt; : ha; vi = hd; vi : v2 = M1 hf; vi = hg; vi : 2v1 + 1 = 3v1 + v2 and 8 gt; gt; lt; gt; : ha; vi lt; hb; vi : v2 lt; 2v2 + 1 ha; vi lt; hc; vi : v2 lt; v1 + 3v2 hf; vi lt; he; vi : 2v1 + 1 lt; v1 hf; vi lt; hh; vi : 2v1 + 1 lt; M2 : (8) For the solution v = (?M1+1; M1; 1) of the linear system, the third inequality yields M1 gt; 2. In Table1 , we list the results of the edge-edge combinations and the constraints they imply.... ..."

### Table 3: The twelve types of cells in the fcc honeycomb, showing numbers of vertices, edges, faces (v, e, f), the number per fcc cell (Ni), and their volumes, probabilities and second

2003

"... In PAGE 18: ...here are twelve types of cells, P1, . . . , P12, whose parameters are summarized in Table3 and whose incidences are shown in Fig. 5.... ..."

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### Table 3: The twelve types of cells in the fcc honeycomb, showing numbers of vertices, edges, faces (v, e, f), the number per fcc cell (Ni), and their volumes, probabilities and second

"... In PAGE 18: ...here are twelve types of cells, P1, . . . , P12, whose parameters are summarized in Table3 and whose incidences are shown in Fig. 5.... ..."

### Table 3: The twelve types of cells in the fcc honeycomb, showing numbers of vertices, edges, faces (v; e; f), the number per fcc cell (Ni), and their volumes, probabilities and second

2003

"... In PAGE 18: ... This honeycomb is the most complicated we have analyzed and we shall give only a brief description. There are twelve types of cells, P1; : : : ; P12, whose parameters are summarized in Table3 and whose incidences are shown in Fig. 5.... ..."

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