Puzzle Formed of Geometric Pieces Having an Even Number of Equilateral Sides

Many geometric puzzles, adapted to educate children and amuse adults, have been proposed. I have discovered that it is possible to dissect a regular octagon to form at least one irregular octagon and one or more smaller pieces. The dissection is such that each of the smaller pieces takes the form of a rhombus, a square, a regular hexagon, or an irregular hexagon. The parts from eight dissected regular octagons may be assembled to form a large tessellated regular octagon. The puzzle provides an intimate knowledge of geometry and is an amusing and instructive one. By providing the pieces with various colors, beautiful octagonal designs may be made to appear when the puzzle is assembled.

My invention relates to an educational puzzle and, more particularly, to a puzzle having a plurality of geometric shapes adapted, when assembled, to form an octagon.

Educational puzzles of the prior art have been known for many years.

Mason U.S. Pat. No. 232,140 shows squares, triangles, rhombuses, and hexagons dissected into various pieces adapted, when assembled, to form the geometric shape from which the individual pieces were derived. None of the pieces has the form of an irregular octagon.

Bishop U.S. Pat. No. 1,657,736 discloses a puzzle having a plurality of pieces adapted to be assembled into either a star or a cross. None of the pieces has the form of an irregular octagon.

Haliburton U.S. Pat. No. 2,053,001 discloses two sets of shapes adapted to be assembled into an octagon or into an irregular geometric figure. Neither of the two shapes has the form of an irregular octagon.

Lee U.S. Pat. No. 3,178,186 discloses a puzzle, the pieces of which are adapted to be assembled into the form of a square, a hexagon, or a triangle. None of the pieces has the form of an irregular octagon.

Kent U.S. Pat. No. 3,637,217 shows a puzzle formed of triangles, trapezoids, rhombuses, rhomboids, and regular hexagons adapted to be assembled to form a regular hexagon in a number of different ways. None of the pieces has the form of an irregular octagon.

Spiecker U.S. Pat. Des. 265,919 shows a mosaic of a square formed of two irregular hexagons, four triangles, two squares, one rectangle, one rhomboid, one irregular trapezoid, and one irregular pentagon. There is no disclosure of an irregular octagon.

In general, my invention comprises the dissecting of a number of regular octagons to form one irregular octagon and one, two, three, four, or five smaller pieces. The irregular octagon is characterized by having four pairs of equilateral parallel sides. Each of the smaller pieces of the octagon takes the form of a rhombus, a square, a regular hexagon, or an irregular hexagon. Both the regular and irregular hexagons are formed with three pairs of equilateral parallel sides. The irregular hexagon differs from the regular hexagon in that it possesses two adjacent sides forming an angle greater than 180 degrees. The puzzle is formed of eight sets of the pieces of twenty-one dissected regular octagons, each of which regular octagons is dissected in a different manner. Certain of the pieces may be assembled to form a tessellated large octagon, and certain of the other pieces may be assembled to form smaller tessellated large octagons in a large number of various manners.

One object of my invention is to provide an instructional and educational puzzle, formed of geometrically shaped pieces adapted to be assembled in various sets to produce a number of tessellated octagons.

Another object of my invention is to provide a series of geometrically shaped pieces, including an irregular octagon, adapted to be assembled in various ways to produce a regular octagon.

Still another object of my invention is to provide a plurality of pieces, obtained by dissecting a number of regular octagons in different manners, in which certain pieces may be colored so that, when assembled, the pieces will form a regular octagon presenting an attractive and original tessellated design.

A further object of my invention is to provide a puzzle, formed of geometrically shaped pieces, which may be assembled in a large number of different ways, each assembly resulting in a tessellated regular octagon.

Other and further objects of my invention will appear from the following description.

In the accompanying drawings, which form part of the instant specification and which are to be read in conjunction therewith:

FIG. 1 shows a regular octagon dissected to form one irregular octagon, two rhombuses, and one irregular hexagon.

FIG. 2 shows a regular octagon dissected to form one irregular octagon and three rhombuses.

FIG. 3 shows a regular octagon dissected to form one irregular octagon, one rhombus, and one irregular hexagon.

FIG. 4 shows a regular octagon dissected to form one irregular octagon, one rhombus, and one regular hexagon.

FIG. 5 shows a regular octagon dissected to form one irregular octagon, one irregular hexagon, and one rhombus.

FIG. 6 shows a regular octagon dissected to form one irregular octagon, one irregular hexagon, and one rhombus.

FIG. 7 shows a regular octagon dissected to form one irregular octagon and two rhombuses.

FIG. 8 shows a regular octagon dissected to form one irregular octagon, two rhombuses, and two squares.

FIG. 9 shows a regular octagon dissected to form one irregular octagon and two irregular hexagons.

FIG. 10 shows a regular octagon dissected to form one irregular octagon and four rhombuses.

FIG. 11 shows a regular octagon dissected to form one irregular octagon and one irregular hexagon.

FIG. 12 shows a regular octagon dissected to form one irregular octagon and one regular hexagon.

FIG. 13 shows a regular octagon dissected to form one irregular octagon and two rhombuses.

FIG. 14 shows a regular octagon dissected to form one irregular octagon and one rhombus.

FIG. 15 shows a regular octagon dissected to form one irregular octagon and two rhombuses.

FIG. 16 shows a regular octagon dissected to form one irregular octagon and five rhombuses.

FIG. 17 shows a regular octagon dissected to form one irregular octagon and four rhombuses.

FIG. 18 shows a regular octagon dissected to form one irregular octagon and three rhombuses.

FIG. 19 shows a regular octagon dissected to form one irregular octagon, two rhombuses, and two squares.

FIG. 20 shows a regular octagon dissected to form one irregular octagon and three rhombuses.

FIG. 21 shows a regular octagon dissected to form one irregular octagon, two squares, and one rhombus.

FIG. 22 shows one example of a tessellated octagon formed of eight sets of all of the pieces shown in FIGS. 1 through 21.

FIG. 23 shows a regular octagon assembled from eight sets of the pieces shown in FIG. 5.

FIG. 24 shows a regular octagon assembled from eight sets of the pieces shown in FIG. 3.

FIG. 25 shows a regular octagon assembled from eight sets of the pieces shown in FIG. 10.

FIG. 26 shows a regular octagon assembled from eight sets of the pieces shown in FIG. 4.

FIG. 27 shows one set of pieces comprising six irregular octagons, four rhombuses, and one square.

FIG. 28 shows a regular octagon formed of eight sets of the pieces shown in FIG. 27.

More particularly, referring now to the drawings, I have applied the reference numeral 2 to each irregular octagon. It will be observed, by referring to FIGS. 1-21, that each of the irregular octagons has a different form. However, each irregular octagon is formed with four pairs of equilateral parallel sides.

I have indicated each regular hexagon by the reference numeral 4. It will be noted, by referring to FIGS. 4 and 12, that each of the regular hexagons is formed with three pairs of equilateral parallel sides.

I have indicated each irregular hexagon by the reference numeral 6. It will be noted, by referring to FIGS. 1, 3, 5, 6, 9, and 11, that each of the irregular hexagons is formed with three pairs of equilateral parallel sides.

I have indicated the squares shown in FIGS. 8, 19, and 21 by the reference numeral 8.

I have indicated each rhombus by the reference numeral 10. It will be noted, by referring to FIGS. 1-8 inclusive, 10, and 13-21 inclusive, that each of the rhombuses is formed with two pairs of equilateral parallel sides.

In all, there are seventy-six pieces formed by the dissection of twenty-one regular octagons. Eight sets of the seventy-six pieces produce six hundred eight pieces. These can be assembled to form a large tessellated octagon in hundreds of different ways, one example of which is shown in FIG. 22. This is the master puzzle.

Each of the assembled tessellated octagons has an octagonal opening in the center. This opening is indicated by the reference numeral 12.

Referring now to FIG. 23, I have shown a single tessellated octagon formed from eight sets of the pieces shown in FIG. 5, which has been reproduced above FIG. 23 for easy reference purposes.

FIG. 24 shows a regular octagon formed from eight sets of the pieces shown in FIG. 3.

Similarly, the regular octagon shown in FIG. 25 is formed from eight sets of the pieces shown in FIG. 10.

FIG. 26 shows a regular octagon formed from eight sets of the pieces shown in FIG. 4.

In FIG. 27, I have shown six irregular octagons, four rhombuses, and one square as a set. Eight sets of these can be assembled to form a larger regular octagon, one of which is shown in FIG. 28. I have made over fifty different regular octagons with the same group of eight sets of the pieces shown in FIG. 27. Furthermore, different permutations and combinations of pieces may be chosen to make other regular octagons, depending on the ingenuity of the user.

It is to be understood that, while I have shown only four examples of regular octagons made from eight sets of a single dissected octagon, twenty-one different octagons may be formed--namely, one from eight sets of the segments from each of the twenty-one octagons, the dissections of which are shown in FIGS. 1-21 inclusive.

The pieces of the puzzle may be constructed, as known to the art, from cardboard. I have constructed my puzzle by making blocks having the shape of identical regular octagons from 1/4-inch foam-core board. I have subdivided the octagonal blocks, as shown in FIGS. 1-21, into segments. A number of segments form a group of parts. Depending on the manner in which the subdivision is performed, the segments, besides one irregular octagon, may number one, two, three, four, or five. A group can be formed of a number of like segments or of a number of different segments, as has been pointed out above. If desired, a felt-lined surface, on which the puzzle can be assembled, may be provided. Each of the irregular octagons may be colored in twenty-one different colors. The rhombuses, squares, regular hexagons, and irregular hexagons may be colored in black, white, and shades of gray. The coloring is optional. When the puzzle is assembled into an octagon, it will present a beautiful, artistic pattern, adding to the recreational and educational value of the puzzle. The geometric shapes arouse the curiosity inherent in their design.

It will be seen that I have accomplished the objects of my invention. I have provided an instructional and educational puzzle, formed of geometrically shaped pieces adapted to be assembled in various sets to produce a number of different tessellated octagons. I have provided a series of geometrically shaped pieces, including an irregular octagon, adapted to be assembled in various ways to produce a regular octagon. I have provided a plurality of pieces, obtained by dissecting a number of regular octagons in different manners, in which certain pieces may be colored, so that, when assembled, the pieces will form a regular octagon presenting an attractive and original tessellated design. I have provided a puzzle formed of geometrically shaped pieces which may be assembled in a large number of different ways, each assembly resulting in a tesselated regular octagon.

It will be understood that certain features and subcombinations are of utility and may be employed without reference to other features and subcombinations. This is contemplated by and is within the scope of my claims. It is further obvious that various changes may be made in details within the scope of my claims without departing from the spirit of my invention. It is, therefore, to be understood that my invention is not to be limited to the specific details shown and described.