Visualising the Boolean Algebra $\mathbb{B}_4$ in 3D (2016), p. 291
by Smessaert, Hans; Demey, Lorenz

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Caption

The RDH and NTH visualisations of the Boolean algebra $\mathbb{B}_4$.

Logic

Aristotelian family

Classical Sigma-7

Boolean complexity

4

Number of labels per vertex (at most)

1

Uniqueness of the vertices up to logical equivalence

Yes

Errors in the diagram

No

Geometry

Shape

Rhombic Dodecahedron (irregular)

Colinearity range

0

Coplanarity range

0

Cospatiality range

2

Representation of contradiction

By central symmetry

Vertex description

Conceptual info

Yes

Mnemonic support (AEIO, purpurea ...)

No

Form

dots

Label type

symbolic

Symbolic field

bitstrings

Contains partial formulas or symbols

No

Contains protobitstrings

No

Bitstring length

4

Edge description

Contains definitions of relations

No

Form

solid lines

,

none

Has arrowheads

No

Overlap

No

Curved

No

Hooked

No

As wide as vertices

No

Contains text

No

Label type

none

Style

Diagram is colored

Yes

Diagram is embellished

No

Tags

Boolean closed

;

non-contingent formulas

;

Hasse diagram

;

Leuven