Girih Polyhedra with Bow Tie Hexagon

These girih polyhedra are heptakaidecahedrons, but they include bow tie concave hexagons where my first version had elongated hexagons, and the second version had rhombi. The pentagon and elongated hexagon are decorated with the girih tile pattern. A similar pattern continues across the triangles.

 Heptakaidecahedron with Girih Pattern

 Heptakaidecahedron

 Heptakaidecahedron Wireframe Girih Pattern

Girih Polyhedra with Rhombus

These girih polyhedra are heptakaidecahedrons, but they include rhombi where my first version had elongated hexagons. The pentagon and rhombus are decorated with the girih tile pattern. A similar pattern continues across the triangles.

Heptakaidecahedron with Girih Pattern

Heptakaidecahedron

Heptakaidecahedron Wireframe Girih Pattern

Girih Polyhedra Pattern

This pattern is from twenty heptakaidecahedrons decorated with girih tile strapwork, and aligned side-by-side. The heptakaidecahedron is a seventeen sided, geometric solid with two girih tile pentagonal faces, five girih tile elongated hexagon faces, and ten isosceles triangles. In this pattern, the three dimensional solids are in five rows of four each heptakaidecahedrons with each alternating row rotated by 180 degrees, and viewed in perspective.

These are the same heptakaidecahedrons at a different scale, and rotating.

Girih Polyhedra

These images are stills from an animation of rotating girih polyhedra. The two polyhedra shown here are a dodecahedron and a heptakaidecahedron. Both of these include faces that are from the girih tile set. The heptakaidecahedron is a seventeen sided geometric solid with two girih tile pentagonal faces, five girih tile elongated hexagon faces, and ten isosceles triangles. The triangles are not original girih tiles. The dodecahedron is a platonic solid, with twelve sides of regular pentagons. The girih tile faces can be decorated with girih lines to create a three dimensional girih pattern.

In one important sense applying girih patterns to polyhedra defeats the purpose of the girih pattern system. That is, girih tiles are designed so that the interior decoration lines continue across boundaries, tangentially. When the lines cross boundaries that are not in the same plane, the continuity is interrupted.

Dodecahedron with Girih Pattern

Dodecahedron

Dodecahedron Wireframe Girih Pattern

Heptakaidecahedron with Girih Pattern

Heptakaidecahedron

Heptakaidecahedron Wireframe Girih Pattern