Rhombiyurt
 Zintaglio Arts / Project Contact: Matt Brand 


A rhombiyurt is a strip-foldable kirigami dome.


Geometry

The rhombiyurt is based on the rhombic triacontahedron (RT), a sphere-like polyhedron made of identical diamond-shaped faces. The RT can be "peeled" like an orange into a continuous strip of panels that folds neatly into a compact package. To design a rhombiyurt: (1) slice the RT below the equator, (2) choose a peeling of the upper half that offers a convenient unfurling motion, (3) add hinges along the strip to enable an accordion-like fold.

An RT peeling (viewed from underneath), used in the animation at top.
Seams are black; interior hinges are blue, exterior hinges are red.
Hinges alternate along the strip to enable an accordian-like fold.

The RT isn't the only "strip-foldable" shape -- see discussion of theory and variations at bottom.

As Shelter

Two 13' (4 meter) diameter rhombiyurts have been our shelter of choice at Burning Man in recent years. With a little practice they can be set up or taken down by two people in <15 minutes (or one person if the air is still).

Rhombiyurts after a dust storm. The one at right has velcro edge flaps along the seams and requires no tape for deployment.

A rhombiyurt requires significantly less material than a full-sized hexayurt, but provides a more pleasant room-like interior with ample headroom, better thermal regulation, and superior high-wind stability (due to roundness). Plus, it looks good.

Construction

Here is a one-page construction guide (PDF) and build notes. Some pictures from the build:

Getting ready: Cutters, tapes, velcro, instructions.
The paper model (cut out from the instructions) is useful for practicing set-up and break-down.
Not shown: 10 sheets of 4'x8' insulating foam.
A cutting jig rigged up for squaring insulation foam and cutting out diamond-shaped panels.
The T-slot aluminum and accessory hardware comes from decommissioned factory enclosures which can be bought cheaply online.
Cut panels for the non-beveled rhombiyurt.
From left to right: 5 diamonds for the peak; 5 "orphans" and 5 "stumps" that will be joined to make 5 more diamonds for the roofline; and 10 extra-tall wall panels.
For the 1' shorter "easy" rhombiyurt, just use the stumps as walls and discard the orphans.
Cutting an 18° edge for the beveled rhombiyurt.
A rig to hold beveled panels at a 36° angle while taping interior hinges.
Beveled panels positioned and tacked for interior hinge taping. This makes a 2-panel "book".
Final assembly of the accordion-folded rhombiyurt by joining "books" with exterior tape hinges.
A tower of scrap foam supports a book while it is hinge-taped to the panel on top of the stack.
Unfurling the accordion.
About to flip the roof peak (at left) onto the already rigid walls (at right).
The roof nestles right into place and makes the walls more rigid.
Surprisingly sturdy even though nothing is holding the seams together other than gravity and friction.
Getting ready to add velcro seam flaps to the (folded up) beveled rhombiyurt.
Note the small triangles sticking out of the diamond at left. These are the bottoms of the extra-tall wall panels.
Two tall rhombiyurts in custom boxes loaded into a shipping container.
The box bump-outs accommodate the extra-tall wall panels.
Note that the 1' shorter "easy" rhombiyurt folds to a perfect diamond.
The (non-beveled) rhombiyurt with an H12 hexayurt behind it.
Both accommodate 3 beds. The rhombiyurt is taller but sheds wind load better.

Please note: Rhombiyurt construction requires more care and planning than a simple hexayurt build. Precise cuts and a well thought out work plan will make a big difference. Measure twice and practice each operation on scrap before doing the real thing.

Theory and Variations

The rhombic triacontahedron is not the only strip-foldable polyhedron, but it occupies a sweet spot for personal shelters because the panel size is large enough to accommodate (or be) a door, yet small enough that the folded package can be moved around by one person. All Platonic and non-pentagonal Catalan solids can be made to work, notably the disdyakis triacontahedron and disdyakis dodecahedron which offer a zipperable seam and would scale well to larger domes.

More generally: A polyhedron is peelable iff its dual graph has a Hamiltonian path; the peeled strip is neatly foldable iff the polyhedron has reflective symmetry over all hinged edges. Any polyhedron can be made peelable with face cuts (Proof: Add edges to triangulate any non-convex faces, then add an edge from from the center of each edge to the center of each face. This yields a degree-4 dual graph, which always has a Hamiltonian path). A slicing of a peelable polyhedron (e.g. to make a dome) will remain peelable if the sliced faces form one or more edge-connected rings. (Proof: The Hamiltonian path is broken into segments by the slicing but since it is non self-crossing, segment ends can be paired and linked around each ring to restore Hamiltonicity.) Some polyhedra don't have edge-peelings that can be laid flat, but any peeling can be folded into a stack whose noon shadow is smaller than the polyhedron's biggest face (by introducing hinges into faces as needed). A conjecture: Every convex polyhedron has a zipperable subdivision peeling that requires no further hinging to fold into a stack with a compact shadow.

Design by Zintaglio Arts. See some of our past and future BM projects: Mutatis Mutandis, Virascope Alpha, Gnomon and  Virascope, FOXP

© 2014-2019 Matt Brand. All rights reserved. Trademark & patents pending.