But there are differences. If we clockwise pass the sides of the rhombic octiamond the color combinations of each side can be denoted by a-b. To get a match in a construction neighboring sides must be a-b and b-a, whereas the single colors at the sides of the diamonds must be equal. Furthermore there are octiamond pieces which are equivalent under reflection but the corresponding diamond pieces are not. This is also true vice versa. Click the numbers of pieces to get some constructions.

Colors | Flip Type | Number of Pieces | Total Number of Triangles |
Constructions |
---|---|---|---|---|

n | one-sided | (n^8+n^4)/2 | ||

two-sided | (n^8+3n^4)/4 | |||

2 | one-sided | 136 | 1088 | 34x16 parallelogram |

two-sided | 76 | 608 | 38x8 parallelogram | |

3 | two-sided | 1701 | 13608 | 3-fold parallelograms, hexagonal ring, parallelograms, rhomb with similar hole |

The 68x8 parallelogram cannot be constructed. Rotate the pieces so that two sides are horizontal and the other ones have a positive slope. Only the horizontal sides can be used for the long sides of the parallelogram but the number of suitable pieces is too small.

The 54x42 parallelogram. All three pictures are here

The 126x18 parallelogram. All three pictures are here

The 162x14 parallelogram. All three pictures are here

At last I tried to construct a hexagonal ring of size 48 with a hexagonal hole of size 6. Since the above method can't be applied the solution is much more difficult to get.

A SVG-file for the construction is here

Taking diamonds and 9 single colors the rendering of the construction looks more colorful. You can see that matching colors are red-red, green-green, violet-violet, lime-teal, yellow-blue, aqua-fuchsia.

A SVG-file for this picture is here

To show parallelograms of size 126x54 and 162x42 I used a different rendering.

If we omit the piece with all eight edge units colored yellow we can get a rhomb with a rhombic hole. The omitted piece may be placed in the center of the hole.

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