Hexagonal Bipyramid Fractal
--- A fractal with 6 square projections ---

The models are at the entrance hall of

Kyoto University museum.


There are a lot of I-cubes, objects with square projections in three orthogonal directions just like a cube.

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.

Here is an applet to rotate this object along with x, y, and z axis.

Please enjoy its view from many directions.

When you select Triangular in the radio button, you will have another fractal, called triangular antiprismoid fractal , with three squrea projections,

References:
Copyright © 2006, 2007, 2008 Hideki Tsuiki. All rights reserved.