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Tetrahex Puzzles

These puzzles use a full set of seven tetrahexes. These pieces cover an area of 28 unit hexagons.

 

Geometric Forms

Use all the pieces to make a symmetric pattern. Click the images below to see example puzzles with solutions.
	Type of Symmetry
	Ternary & Horizontal	Ternary & Vertical	Trirotary	Double Bilateral	Birotary	Horizontal	Vertical
Solutions	2	1	20	76	1000s	1000s	1000s

Use any three pieces to make a symmetric pattern. Click the images below to see example puzzles with solutions.
	Type of Symmetry
	Ternary & Vertical	Double Bilateral	Birotary	Horizontal	Vertical
Solutions	4	15	98	236	126

Butterflies and Propellers

The first butterfly and propeller puzzles have a single symmetric piece removed as a body, with the remaining pieces used to make two identical wings. The final type has a 3-piece body and two-piece wings. Click the images below to see a full set of puzzles with solutions.
Body
Butterflies		X
Propellers			X	X

 

Portholes

 

Create a pattern which encloses the maximum number of unit holes. Here are examples for the different types of symmetry. Six holes is maximal even without symmetry. Click the images below to see a set of puzzles with solutions.
Type of Symmetry
Ternary & Horizontal	Ternary & Vertical	Trirotary	Double Bilateral	Birotary	Horizontal	Vertical
6	3	3	5	6	6	6

 

Tri- and Tetrahex Puzzles

These puzzles use a full set of seven tetrahexes and three trihexes. These pieces cover an area of 37 unit hexagons. For clarity, the tetrahexes are referred to using the usual numbers, with the trihexes labelled "A", "B" and "C".

Geometric Forms

 

Use all the pieces to make a symmetric pattern. Click the images below to see example puzzles with solutions.
	Type of Symmetry
	Full	Sextarotary	Ternary & Horizontal	Ternary & Vertical	Trirotary	Double Bilateral	Birotary	Horizontal	Vertical
Solutions	2	3	56	18	1000s	?	1000s	1000s	1000s

Butterflies &  Twin Propellers

1. Take one tetrahex and one trihex piece to make a symmetric body, with the remaining pieces used to make two identical wings. A solution with mirror symmetry is a butterfly, whilst one with rotational symmetry is a propeller.
Body = tetrahex
+ one of these trihexes
Butterflies
Propellers
2. Take one trihex and all three tetrahexes to make a symmetric body, with the remaining pieces used to make two identical wings.
Body = tetrahex
+ all three trihexes
Butterflies
Propellers
3. Take three tetrahexes and one trihex to make a symmetric body, with the remaining pieces used to make two identical wings.

Triple Propellers

Remove the #4 tetrahex as a body and make three identical wings with the remaining pieces. One wing uses the three listed pieces. Click the images below to see a set of puzzles with solutions.
Body
Wings	12A	12B	12C	23A	23B	23C
Propellers
Wings	25A	25B	25C	26A	26B	26C
Propellers
Wings	27A	27B	27C
Propellers

Portholes

Create a pattern which encloses the maximum number of unit holes. Here are my best results for the different types of symmetry. Click the images below to see example puzzles with solutions.
Type of Symmetry
Full	Sextarotary	Ternary & Horizontal	Ternary & Vertical	Trirotary	Double Bilateral	Birotary	Horizontal	Vertical
X	6	6	6	9	10	10	10	10

 

Complete the Shape

 

Take three tetrahex pieces, and make any connected shape of 12 hexagons. Use the seven remaining pieces to complete the shape so that the complete pattern is symmetric in some way.

Mono-Tetrahex Puzzles.

These puzzles use a full set of seven tetrahexes, three trihexes, the dihex and monohex. These pieces cover an area of 40 unit hexagons.