01 · Sizing

How big does the sphere need to be?

A sphere is a wonderful pressure hull and an awkward house: you live on flat floors, but the shell curves away at every level. So we size the home the honest way - fit the largest cube that lives inside the internal sphere, treat the curved volume outside it as dead space, and only then stack floors. It is conservative on purpose, and it makes the trade-offs visible.

AThe inscribed-cube model

The largest cube inside a sphere has its space diagonal equal to the diameter, so its side is s = 2R/√3 - about 1.15 R. The volume beyond each of the six faces is a spherical cap. Those six caps overlap along the 12 edges and 8 corners, so the honest excluded volume is sphere − cube, not six separate caps. The single bottom cap is clean and non-overlapping, which is exactly why it makes a tidy ballast tank.

Internal diameter Wall thickness Floor slab thickness Room height (clear)

Honest result worth staring at: at 8.5 m internal Ø the cube is only ~4.9 m tall, so a 0.2 m slab + 2.3 m ceiling (2.5 m pitch) fits one strict cube floor of ~24 m², not two. To get the second full floor inside the cube you need either a bigger sphere (~8.7 m internal Ø), a tighter pitch (thinner slab or ~2.25 m ceilings), or you push the upper bedroom out as a mezzanine into the top cap. Drive the four sliders and watch the floor count flip - that threshold is the real design decision behind "two-floor, two-bedroom".

BWhere the volume goes

A sphere of 8.5 m internal diameter holds ~322 m³ of air. Here is how the inscribed-cube model spends it.

Zone	What it is	Reference volume	Use
Inscribed cube	Rectilinear living envelope, side 2R/√3	~118 m³	Floors + rooms
Bottom cap	Single clean cap below the cube floor	~37 m³	Ballast tank (~38 t seawater)
Top + 4 side caps	Curved volume above and around the cube	~166 m³	Services, storage, buoyancy trim, curved built-ins
Excluded total	sphere − cube (de-overlapped)	~203 m³	Not counted as livable

The cube is deliberately pessimistic. If you want the floor area back, the plates can be pushed out past the cube toward the shell - they become octagons or circles that shrink near the poles, gaining usable m² at the cost of messier joinery and a curved perimeter wall. The cube number is the floor you can promise; the sphere-hugging number is the ceiling you can chase.