The polyhedron explained here has square projections. But not in
three but in SIX directions.
That is, it is a double I-cube .
It is a hexagonal bipyramid with
12 isosceles triangular faces with the height 3/2 of the base.
When it is looked at from its faces, it looks square. Therefore, it has 12 square appearances.
Consider an object composed of nine small hexagonal bipyramids which
are dilations of a hexagonal bipyramid with the ratio 1/3 and with the
fixedpoints the 8 vertexes and the center of it.
It looks square from the 12 directions.
It is true for the object composed of 81 pieces obtained by one more
repetition of the dilations.
It is also true for the limit object.
It is a fractal object with the fractal diemnsion two and it has square projections
in six directions.
Please enjoy its appearances in many directions.
Please enjoy its view from many directions.