Hexagon Bin Key

[Mirtha Shikles]

Aregular hexagon is defined as a hexagon that is both equilateral and equiangular. It is bicentric, meaning that it is both cyclic (has a circumscribed circle) and tangential (has an inscribed circle).

The common length of the sides equals the radius of the circumscribed circle or circumcircle, which equals 2 3 \displaystyle \tfrac 2\sqrt 3 times the apothem (radius of the inscribed circle). All internal angles are 120 degrees. A regular hexagon has six rotational symmetries (rotational symmetry of order six) and six reflection symmetries (six lines of symmetry), making up the dihedral group D6. The longest diagonals of a regular hexagon, connecting diametrically opposite vertices, are twice the length of one side. From this it can be seen that a triangle with a vertex at the center of the regular hexagon and sharing one side with the hexagon is equilateral, and that the regular hexagon can be partitioned into six equilateral triangles.

Like squares and equilateral triangles, regular hexagons fit together without any gaps to tile the plane (three hexagons meeting at every vertex), and so are useful for constructing tessellations. The cells of a beehive honeycomb are hexagonal for this reason and because the shape makes efficient use of space and building materials. The Voronoi diagram of a regular triangular lattice is the honeycomb tessellation of hexagons.

It follows from the ratio of circumradius to inradius that the height-to-width ratio of a regular hexagon is 1:1.1547005; that is, a hexagon with a long diagonal of 1.0000000 will have a distance of 0.8660254 between parallel sides.

For an arbitrary point in the plane of a regular hexagon with circumradius R \displaystyle R , whose distances to the centroid of the regular hexagon and its six vertices are L \displaystyle L and d i \displaystyle d_i respectively, we have[3]

These symmetries express nine distinct symmetries of a regular hexagon. John Conway labels these by a letter and group order.[4] r12 is full symmetry, and a1 is no symmetry. p6, an isogonal hexagon constructed by three mirrors can alternate long and short edges, and d6, an isotoxal hexagon constructed with equal edge lengths, but vertices alternating two different internal angles. These two forms are duals of each other and have half the symmetry order of the regular hexagon. The i4 forms are regular hexagons flattened or stretched along one symmetry direction. It can be seen as an elongated rhombus, while d2 and p2 can be seen as horizontally and vertically elongated kites. g2 hexagons, with opposite sides parallel are also called hexagonal parallelogons.

A truncated hexagon, t6, is a dodecagon, 12, alternating two types (colors) of edges. An alternated hexagon, h6, is an equilateral triangle, 3. A regular hexagon can be stellated with equilateral triangles on its edges, creating a hexagram. A regular hexagon can be dissected into six equilateral triangles by adding a center point. This pattern repeats within the regular triangular tiling.

From bees' honeycombs to the Giant's Causeway, hexagonal patterns are prevalent in nature due to their efficiency. In a hexagonal grid each line is as short as it can possibly be if a large area is to be filled with the fewest hexagons. This means that honeycombs require less wax to construct and gain much strength under compression.

Irregular hexagons with parallel opposite edges are called parallelogons and can also tile the plane by translation. In three dimensions, hexagonal prisms with parallel opposite faces are called parallelohedrons and these can tessellate 3-space by translation.

Pascal's theorem (also known as the "Hexagrammum Mysticum Theorem") states that if an arbitrary hexagon is inscribed in any conic section, and pairs of opposite sides are extended until they meet, the three intersection points will lie on a straight line, the "Pascal line" of that configuration.

The Lemoine hexagon is a cyclic hexagon (one inscribed in a circle) with vertices given by the six intersections of the edges of a triangle and the three lines that are parallel to the edges that pass through its symmedian point.

If, for each side of a cyclic hexagon, the adjacent sides are extended to their intersection, forming a triangle exterior to the given side, then the segments connecting the circumcenters of opposite triangles are concurrent.[7]

A skew hexagon is a skew polygon with six vertices and edges but not existing on the same plane. The interior of such a hexagon is not generally defined. A skew zig-zag hexagon has vertices alternating between two parallel planes.

A regular skew hexagon is vertex-transitive with equal edge lengths. In three dimensions it will be a zig-zag skew hexagon and can be seen in the vertices and side edges of a triangular antiprism with the same D3d, [2+,6] symmetry, order 12.

There is no Platonic solid made of only regular hexagons, because the hexagons tessellate, not allowing the result to "fold up". The Archimedean solids with some hexagonal faces are the truncated tetrahedron, truncated octahedron, truncated icosahedron (of soccer ball and fullerene fame), truncated cuboctahedron and the truncated icosidodecahedron. These hexagons can be considered truncated triangles, with Coxeter diagrams of the form and .

Scale the pentagon down by hexagon edge length/pentagon edge length (a browser will calculate this for you). You can copy the lengths from the dimension - click on it to open the dimension text for editing and copy it.

after I selected the hexagon > scale >grabbed corner and with mouse was trying to get 100.000000 (dimension text was changing, it was close 100.004354 or so, but never 100.000000, I could zoom in more but in that case the dimension text was missing from view. (with precision 0mm it worked, was easy to match)

thank you for your tips, I have a question about your scale box on the second screenshot, there are numbers 0.85065081167, In my box was only 0.85. how to set precision as high as possible for Scale box? (like we did with Length units) or maybe its because of another version of sketchup?!

Go to Window/Model info/Units/Precision and set the precision as high as possible. It affects the display of lengths but not the internal precision that SU uses, and not just the Scale tool, but all displayed dimensions. I copied the long string of digits from the calculation I asked my browser to perform.

image1068610 114 KB

After making the Charm Square Fabric Tray, I had a brainwave to make a hexagon shaped tray. I love it when an idea works out perfectly. Personally I think the hexagon fabric tray is even cuter than the original square version (see the tutorial for the Charm Square Fabric Tray here). I shared some photos on Instagram earlier in the week and had some requests for a tutorial so have put together some instructions below if you would like to make your own.

The Hexagon Fabric Tray is slightly smaller than the charm square tray. It measures 3 inches across the base at the widest point and 4.5 inches across the top at the widest point (from tip to tip). It is a lovely little size to hold earrings or small items of jewellery. it would also be useful in the sewing room to hold buttons, pins, wonder clips, or mini hexies.

1. Lay the batting down on a flat surface. Position the white linen on top with the right side facing upwards. Position the floral print on top with the wrong side facing upwards. Ensure all the edges and corners are perfectly aligned. Pin the 3 layers together.

2. Stitch around the perimeter of the hexagon using a 1/4 inch seam allowance. Leave a gap of 1.5 inches in one side for turning. Clip the corners, and turn out the right way through the gap in the lining. Poke out the corners using a bamboo skewer or turning tool. Press.

4. Using a hera marker, mark a line that is 1 inch from each outside edge. This will create a smaller hexagon in the centre that measures 3 inches from one side to the other. Stitch along the marked line. Press.

What a cute little dish, I just found you via a link from sewsweetviolet! I love the idea that you blog together as Mother and Daugher. My daughter and I also love to create together, thankfully now she has finished her A levels we should have more time to create together ? Sharon

Thanks Daniela. The seed tags are actually cut from some fabric. It is called Seed Catalogue by Lakehouse Dry Goods. It came out a few years ago but I think they have released some new fabric that is very similar.

Welcome to the forums!

You can create a block with your hexagon, then add a Block Component to the Label Style. Set it so it displays in Tag mode, make sure the size is large enough to hold the Tag.

Unfortunately we were not given the option o include anything other than the number value or text. You will need to manually place the block as needed, and then make sure to add/remove them when edits are made.

That did the trick! The only other thing I have an issue with which I suppose I can deal with is the insertion of the leader. I did not see an option where it asked for that. I attached a video of what I am talking about.

Truly inspiring! Thank you so much for sharing, especially your half-hex pattern, which is brilliant. It may take me years to finish it, but if I work a few hexies in between other projects or when I'm too tired to follow a complex pattern, I'll eventually have a blanket. Hope it's as lovely as yours.

Thanks! And I think that's a great idea. The little hexagons work up really quickly and they're perfect for crocheting on the go (in waiting rooms, on the bus, etc). You could also make something smaller like a pillow case or a wall hanging if you want a quicker project. Either way, it'll be awesome :)

I left a long yarn tail at the end of each hexagon and then used those tails to weave the pieces together. So I just used the tail for the next hexagon I was attaching. Since I used the mattress stitch to sew the pieces together, the colors of the yarn tail aren't very visible either way, so it didn't really matter which color tail I was using.

3a8082e126