Add Data for VTK volume fails

‘Structured Points’ is what Paraview exports me as legacy VTK after reading a VTI file. I do not have a choice. However, I discovered that after some filtering (thresholding) Paraview exports me an ‘unstrucered grid’ as legacy VTK from the same original file.
Still, it cannot be read by Slicer.

Below I copy the ascii version of this type of VTK files (an even smaller subset as posted before):

# vtk DataFile Version 4.2
vtk output
ASCII
DATASET UNSTRUCTURED_GRID
POINTS 64 float
0 0 0 1 0 0 0 1 0 
1 1 0 0 0 1 1 0 1 
0 1 1 1 1 1 2 0 0 
2 1 0 2 0 1 2 1 1 
3 0 0 3 1 0 3 0 1 
3 1 1 0 2 0 1 2 0 
0 2 1 1 2 1 2 2 0 
2 2 1 3 2 0 3 2 1 
0 3 0 1 3 0 0 3 1 
1 3 1 2 3 0 2 3 1 
3 3 0 3 3 1 0 0 2 
1 0 2 0 1 2 1 1 2 
2 0 2 2 1 2 3 0 2 
3 1 2 0 2 2 1 2 2 
2 2 2 3 2 2 0 3 2 
1 3 2 2 3 2 3 3 2 
0 0 3 1 0 3 0 1 3 
1 1 3 2 0 3 2 1 3 
3 0 3 3 1 3 0 2 3 
1 2 3 2 2 3 3 2 3 
0 3 3 1 3 3 2 3 3 
3 3 3 
METADATA
INFORMATION 1
NAME L2_NORM_RANGE LOCATION vtkDataArray
DATA 2 0 5.19615 

CELLS 27 243
8 0 1 2 3 4 5 6 7 
8 1 8 3 9 5 10 7 11 
8 8 12 9 13 10 14 11 15 
8 2 3 16 17 6 7 18 19 
8 3 9 17 20 7 11 19 21 
8 9 13 20 22 11 15 21 23 
8 16 17 24 25 18 19 26 27 
8 17 20 25 28 19 21 27 29 
8 20 22 28 30 21 23 29 31 
8 4 5 6 7 32 33 34 35 
8 5 10 7 11 33 36 35 37 
8 10 14 11 15 36 38 37 39 
8 6 7 18 19 34 35 40 41 
8 7 11 19 21 35 37 41 42 
8 11 15 21 23 37 39 42 43 
8 18 19 26 27 40 41 44 45 
8 19 21 27 29 41 42 45 46 
8 21 23 29 31 42 43 46 47 
8 32 33 34 35 48 49 50 51 
8 33 36 35 37 49 52 51 53 
8 36 38 37 39 52 54 53 55 
8 34 35 40 41 50 51 56 57 
8 35 37 41 42 51 53 57 58 
8 37 39 42 43 53 55 58 59 
8 40 41 44 45 56 57 60 61 
8 41 42 45 46 57 58 61 62 
8 42 43 46 47 58 59 62 63 

CELL_TYPES 27
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11

CELL_DATA 27
FIELD FieldData 1
image 1 27 double
1 1 0 1 1 0 0 0 0 
1 0 0 0 0 0 0 0 0 
1 0 0 0 0 0 0 0 0 

METADATA
INFORMATION 0