Beadwork, Polyhedra, Tutorials

Truncated Octahedron Hyparhedron

Here are some brief instructions for the truncated octahedron hyparhedron. This is actually a pretty simple shape to make. It’s just 4-hats joined together with a few extra warped squares. If you know how to zip together warped squares to make a star you can use the same method here! My warped squares are 7 rows in total, and I make them out to row 6 then use row 7 to zip to any other squares as needed.

truncated_octahedron_beadmechanics

First join four warped squares with 2 brown sides and 2 green sides into an upside-down 4-hat – that is, with all the points in the centre pointing downwards. This will be one of the square faces you can see in the photo above.

trunc_octa1_beadmechanics

Here’s a diagram for the individual warped squares that make up the 4-hat:

warped_square

Make the first square completely all the way out to row 7 and stitch in the threads (the photo is in red and white instead of brown and green – sorry!):

TruncatedOctahedronStep1_BeadMechanics

Now make a second square out to row 6 and join it to the first square on one brown (or red!) side as part of row 7 as shown (note I’m working anticlockwise around the square):

TruncatedOctahedronStep2_BeadMechanics

Finish the round and weave in the end – you should now have two squares joined together like this:

TruncatedOctahedronStep2b_BeadMechanics

Make a third square out to row 6 and again join to one of the others on one brown (/red) side as part of row 7 as shown:

TruncatedOctahedronStep3_BeadMechanics

When this square is completed it will look like this:

TruncatedOctahedronStep3b_BeadMechanics

Make a fourth square out to row 6 and this time join it to the two remaining brown (/red) edges from the previous squares using row 7:

TruncatedOctahedronStep4_BeadMechanics

When this square is complete you will have a finished 4-hat like the one below!

TruncatedOctahedronStep4b_BeadMechanics

Here it is from the side – the centre points downwards (so technically it’s an upside-down 4-hat!):

truncated_octahedron1_beadmechanics

Make five more of these so that you have six identical 4-hats in total. The warped squares here are all edges of a square face on the finished shape.

Now make a completely green warped square out to row 6 (I use the same silver diamond pattern as before, but all the sides just have the same background colour). Step up for row 7 and zip it on all sides to two of the 4-hats, as shown on the left of the diagram below. The centre pyramid of both 4-hats should be pointing downwards. (Note that I’ve shown this new warped square in blue rather than green!) The new warped square is an edge of a hexagonal face. To show the shape flat I’m going to draw the warped squares slightly distorted (as on the right of the diagram) from this point onwards.

trunc_octa2_beadmechanics

Here are two 4-hats and a warped square ready to be joined together:

TruncatedOctahedronStep5a_BeadMechanics

Here are the first two sides being joined together:

TruncatedOctahedronStep5b_BeadMechanics

And here’s the piece from the other side showing last two sides being joined together:

TruncatedOctahedronStep5c_BeadMechanics

When the join is complete the beadwork will look like this:

TruncatedOctahedronStep5d_BeadMechanics

Here’s another in-progress photo from slightly later in the construction outlining how this square fits between two of the upside-down 4-hats:

truncated_octahedron3_beadmechanics

(Note though that this particular photo used a slightly different order for joining the squares than the instructions here!)

Repeat this step three more times to join three more 4-hats around the first, as shown in the diagram below:

trunc_octa3_beadmechanics

Now join in four more warped squares around the edge of the shape connecting some of the remaining edges of the 4-hats as shown below:

trunc_octa4_beadmechanics

The diagram above looks pretty distorted but in reality the warped squares will fit easily into place.

Turn the beadwork over. There will be a space for the remaining 4-hat, which should be joined in using 4 more green warped squares, as shown below:

trunc_octa5_beadmehanics

Once all these joins are finished the hyparhedron is complete. Sorry the instructions are a bit brief but if you have any questions just ask and I will try and help!

 

 

© Copyright 2019 Patricia Verrier. All rights reserved.

These instructions are for personal use only. Please contact me if you require more information.

3 thoughts on “Truncated Octahedron Hyparhedron

  1. This is a foolish query, perhaps, but could you possible show one warped square in a diagram and then two together? I’ve done lots with warped squares, but I’m having trouble recognizing them in your photo, I.e. you say four warped squares for the start but I don’t see how the Herringbone is situated in the red and gold diagram that works.

    I’d love to make this. Thanks for sharing.

    Phyllis Dintenfass

    Sent from my iPad

    >

    Like

    1. Sorry about the lack of photos! I am going to take some of the first few steps this week and will definitely include this! (I completely forgot to take photos when I first made it but wanted to get something written up for it at least!) The herringbone is partly just where the colour change is, which perhaps makes it not the easiest to see…

      I traced over them on a photo in the previous post if that helps for now?

      Like

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