As a continuation of my Tessellation project, this assignment challenged me to reexamine the previous assignment in terms of parent geometries, symmetries, proportional types and proportions of faces, edges and vertices then express and/or represent the two-dimensional tessellating unit in three-dimensional form.
My 2D tessellating unit is composed of two Cairo pentagons, two equilateral triangles and four isosceles right-angle triangles.
Each Cairo pentagon has five vertices and two right angles. The Cairo pentagon in my original drawing is composed of four short edges approximately measuring 0.6” and one long edge approximately measuring 1”. The ratio of the four short edges to the long edge is about 1.66, which is about equal to the golden ratio, 1.62.
The tessellating unit as a whole is symmetrical along both the vertical and horizontal axes. This is an example of static symmetry.
To represent my 2D partee in 3D, I created a three-dimensional unit that forms a pentagon shape when viewed on its side using equilateral triangles and right angle triangles.I found that extending the equilateral faces forward and the right-angle faces backward enabled me to create a 3D form that represents my 2D parti.
After aligning the tetrahedrons, I connected the edges of my two right-angle tetrahedrons to form the Cairo pentagons in the middle.
Hence, my final 3D form expresses the geometric parti of the previous assignment as well as the internal relationships I discovered.
