Zome Primer — Steve Baer (1970)

Steve Baer — Zomeworks Corporation, Albuquerque, New Mexico — August 1970

Signed: S.C.B., Albuquerque, August 1970.

Preceded by Dome Cookbook (Lama Foundation, New Mexico, 1968).

Note: The epub’s appended index appears to be from a separate work (likely Buckminster Fuller), included in error during digitization. The index content below the Bibliography is not part of this book.

Preface

This booklet has first an elementary explanation of the geometry of Zonohedra, then a more difficult account of the growths of the thirty-one zone star. This system, based on the 31 lines that pass through the center of an icosahedron and either a vertex, edge midpoint or face midpoint is new and unusual.

I have applied for a patent on this structural system. The patent is assigned to Zomeworks Corporation. The predecessors of this system are the octet truss and the MERO space grid system.

The forms possible using this system are limitless; there is no attempt here to explore these possibilities—the examples shown are small probings. The booklet describes the mathematics of the process that creates these limitless forms.

Collaborators named in the preface:

Jim Welty and Robert Ford — designed the Robert Ford residence framework
Berry Hickman (Zomeworks) — shallow rectangular trusses and the plastic ball joint used in models
Otto Jung, Design Industries, Albuquerque — 6-zone aluminum joint
Ken Leonard — layout
Holly Baer — editorial assistance

Chapter 1: Zomes, Domes and Clusters

What Are Zomes?

A Zome is a man-made structure derived from zonohedra. The zones of the zonohedron may be stretched or shrunk or removed to produce, if desired, an asymmetric dome shaped structure.

Zomes may be single or clustered.

Zomes can cluster together like soap bubbles. Their zones can be stretched, shrunk, or omitted completely to make the various zomes’ different shapes and sizes. The zomes can also pack several layers deep.

Zome vs Geodesic Dome

A geodesic dome is a structure which closely follows the shape of the sphere and whose edge lengths closely follow the path of great circles on the sphere… The geodesic dome, because of its shape, and the arrangement of its structural members is extremely strong, but its uses are limited because of the inflexibility of its shape. It is always part of a sphere—a low bubble or a high bubble—its floor is always a circle—any variation would destroy the structural properties of the geodesic dome. The geodesic dome, if it is large and composed of many edges and joints, has many different edge lengths. It is complicated in structure and simple in shape. Zomes are simple in structure and complicated in shape.

Chapter 2: Zonohedra

Definition

A zonohedron is a convex solid, all of whose faces are polygons with edges in equal and parallel pairs.

A zone of edges is a band of parallel edges which circles the solid. Every edge belongs to a zone.

Key zonohedra:

Rhombic Triacontahedron — 30 faces, 6-zone system, 15 face planes
Enneacontahedron — 90 faces, 10-zone system, 45 face planes
Truncated Octahedron — associated with the 6-zone star

The number of face planes for an n-zone system: X = n(n−1)/2. Total faces (both sides): n(n−1).

Cells

Every zonohedron divides into parallelpiped cells. Sets of three different lines form one cell:

Triacontahedron: 20 cells (10 acute + 10 obtuse parallelepipeds)
Enneacontahedron: 120 cells (5 types: A, B, C, D, E)

Chapter 4: Clustering

The triacontahedron (30-face, 6-zone zonohedron) is the base unit for clustered zomes. Two triacontahedra fuse through a skew hexagon. Additional zomes attach similarly — the “triple cluster complex” Baer describes building at Drop City in 1968 is this arrangement: three or more triacontahedra fused through shared skew hexagons.

Clusters can contain units of different sizes — a triacontahedron of edge A clusters with one of edge A·τ⁻¹ (where τ is the golden ratio).

Chapter 5: Stretching a Zone

Zones (bands of parallel edges) can be stretched to alter shape without changing any angles. This allows buildings of different shapes from the same component types. The Baer House cluster uses stretched zones to create the varied south-facing facets documented in the photographs.

Chapter 8: The 31-Zone Star

The structural innovation of the book: a star based on 31 lines through the center of an icosahedron — 6 A lines (through icosahedron vertices), 10 B lines (through dodecahedron vertices / icosahedron face midpoints), 15 C lines (through edge midpoints). This produces six section types (R, S, T, V, X, Y) and 242 possible face planes.

Patent applied for, assigned to Zomeworks Corporation. Predecessors: octet truss (12-zone), MERO space grid (13-zone). The 31-zone system is more flexible than either.

Chapter 15: Hardware

A lines = 40″; C lines = 42″ (C = A·1.0514622). The 6-zone aluminum joint was manufactured by Otto Jung of Design Industries, Albuquerque. A ball-and-threaded-hole joint is ideal but expensive; flange joints are cheaper but require careful orientation design.

Bibliography (selected)

Baer, Steve — The Dome Cookbook — Lama Foundation, New Mexico — 1968
Borrego, John — Space Grid Structures — MIT Press — 1968
Coxeter, H.S.M. — Regular Polytopes — Macmillan — 1948 & 1963
Cundy and Rollett — Mathematical Models — Oxford — 1951 & 1961
Thompson, D’Arcy — On Growth and Form — Cambridge — 1942 & 1963

Source: Steve Baer, Zome Primer: Elements of Zonohedra Geometry, Zomeworks Corporation, Albuquerque, August 1970. Text extracted from epub (digitized 2024-12-15). File: 1970-08-01-zome-primer.epub