▸ BIG IDEA (ELI5)
6 ways to pack atoms (or data) into a crystal.
FCC, BCC, HCP, diamond cubic, simple cubic, hexagonal.
The universal packing problem: how do you fill space most efficiently?
Nature solved this 14 ways (Bravais lattices) but these
6 are the archetypes. The fleet's data structures follow the
same packing rules — PSGraph is a face-centered stack,
the adelic rings are hexagonal close-packed, ARB trees are diamond cubic.
Every lattice has a packing fraction, a
symmetry group, and a coordination number
(how many neighbors each atom touches). The fleet maps each silo to its lattice type.
▸ ELEMENT CARDS
L·1
FCC
FACE-CENTERED CUBIC
Closest packing cubic
PF = 74.05%
CN=12 · Oh symmetry · a=b=c · α=β=γ=90°
Most efficient cubic packing. Cu, Al, Au. Fleet analog: PSGraph edge adjacency — each node has 12 near-neighbors.
L·2
BCC
BODY-CENTERED CUBIC
Iron backbone lattice
PF = 68.02%
CN=8 · Im3m · a=b=c · α=β=γ=90°
Rigid with body atom. Fe, W, Cr. Fleet analog: LHVCP cluster — control plane in center, 8 worker nodes around it.
L·3
HCP
HEXAGONAL CLOSE-PACKED
Layered tight packing
PF = 74.05%
CN=12 · P6₃/mmc · c/a=1.633
Equal packing to FCC but hexagonal. Mg, Ti, Zn. Fleet analog: Adelic concentric rings — each L-layer stacks on the one below.
L·4
DIA
DIAMOND CUBIC
Tetrahedral covalent
PF = 34.01%
CN=4 · Fd3m · two interpenetrating FCC
Open but extraordinarily strong. C, Si, Ge. Fleet analog: joffe-math theorem tree — each node has exactly 4 proof children.
L·5
SC
SIMPLE CUBIC
Primitive square lattice
PF = 52.36%
CN=6 · Pm3m · rarest in nature
Only Polonium naturally. Lowest efficiency but maximum regularity. Fleet analog: MECRDS CRQ table — rigid grid, no shortcuts.
L·6
HEX
HEXAGONAL SIMPLE
2D layer stacking
PF = 60.46%
CN=8 · P6/mmm · graphite layers
Graphene layers. Strong in-plane, weak between planes. Fleet analog: GPU framebuffer — massive parallel rows with thin bus between layers.
▸ REACTOR DEMO — Lattice Packing Comparator
LATTICE TYPES · PACKING FRACTION VISUALIZER · CLICK TO SELECT
Click a lattice type above to inspect its properties.
▸ INSTRUMENT — Packing Efficiency Comparison
FCC Face-centered cubic
74.05% PF
HCP Hexagonal close-packed
74.05% PF
HEX Hexagonal simple
60.46% PF
SC Simple cubic
52.36% PF
BCC Body-centered cubic
68.02% PF
DIA Diamond cubic
34.01% PF ⚡
▸ DIA has lowest PF but highest bond strength — open structure trades density for rigidity
▸ BONIXER — 4-Layer Assessment
L0 · GEOMETRY
96
Symmetry accuracy
L1 · MAPPING
82
Fleet analogs
L2 · COMPUTE
78
Data structure fit
L3 · EXTEND
61
New lattice types