SPHERICAL MONOTILES
ABOUT SPHERICAL MONOTILES
LIST OF OCTAHEDRAL MONOTILES
CUBE & ESCHER SOLID
Rhombohedral Monotiles
Rhombohedra are composed of a trigonal antiprism bound by two irregular-tetrahedra.
The cube is a unique rhombohedron where each face is a regular square.
A Rhombohedra can be formed by stretching the two polar vertices of a cube in opposite directions along its diagonal axis, transforming each square face into identical rhombi.
also referred to as:
Trigonal Trapezohedron or Trigonal Gyroelongated Bipyramid
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Filling Space with Rhombohedra
Periodic tilings of rhombohedra produce the trigonal
trapezohedral honeycomb (Rhombohedrille).
EXTENDING STUDY OF TILING (2-TILE TESSELATIONS)
an irregular version of all cubic space filling tessellations can be found inside of Rhombohedrille.
Example: An Irregular- Cuboctahedrille (space filling tessellation) can be derived by truncating each rhombohedron into Irregular-Cuboctahedra and Irregular-Octahedra.
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LIST OF RHOMBOHEDRAL MONOTILES