snow-capped-sonobe-1-hexaugmented-K4-6Q4(E4)

When Daniel Kwan commented on this object a couple of weeks ago, he proposed an interesting idea:

Nice shape design. The "craters" on each octagonal face being square cupolae implies another potention shape design. You could take 6 square bicupolae (of the ortho or gyro type, whichever is more aesthetic), and join them with cubes as well.

This picture is the result: six square (ortho)bicupolae connected together by 12 cubes. I needed 240 Sonobe units and perhaps a dozen hours (spread out over 2 weeks) complete this object.

I had initially planned to call this a "hexaugmented great rhombicuboctahedron", but it turns out that this family of objects already has a name: The "K4 World!" In fact, this picture is just the third image on the page with six square cupola caps on the ends to "simulate" the octagons. Since Norman Johnson's convention was to call polyhedra "augmented" whenever he stuck cupolae on top of them, I've decided to call this shape a hexaugmented K4 / 6Q4(E4).

Obviously, I'm not the first to try sticking smaller polyhedra together to create bigger ones. B.M. Stewart might have been, and this family of shapes is called the "Stewart toroids" as a result. A quick search for that term on flickr shows that the geomag folks have also beat me to the punch.

Ah well, at least I'm the only one using paper!

Some rights reserved

Taken on: September 18, 2008

Tags:

modular origami

sonobe module

stewart toroid

k4 world

sonobe « less

Sets appears in: • Finished Sonobe Polyhedra

Groups appears in: • Modular origami • Origami Sonobe

Camera: Panasonic DMC-FX3, f/2.8, 1/15 sec, 5.8mm, ISO 125 (more info) (hide info)

Camera:	Panasonic DMC-FX3
Aperture:	f/2.8
Exposure Time:	0.067 sec (1/15)
Focal Length:	5.8mm
ISO:	125
Exposure Bias:	0 EV
Flash:	Off, Did not fire
Exposure Program:	Program AE
Exposure Mode:	Auto
Metering Mode:	Center-weighted average
White Balance:	Auto
Gain Control:	Low gain up
Color Space:	sRGB
Software:	GIMP 2.4.4
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