# Algebraic Aspects of Duality Diagrams (2012), p. 302

by Demey, Lorenz

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### Caption

- (a) The duality cube for $\mathbb{G}_8$. (b) The two squares for {I, L, M, LM}, and (c) for {I, L, RM, LRM}. (d) One of the two tetrahedra for {I, LR, RM, LM}.

- Aristotelian family
- Sigma-4 Graph
- Boolean complexity
- 4–16
- Number of labels per vertex (at most)
- 1
- Uniqueness of the vertices up to logical equivalence
- Yes
- Errors in the diagram
- No
- Shape
- Cube (regular)
- Colinearity range
- 0
- Coplanarity range
- 0
- Cospatiality range
- 0
- Representation of contradiction
- By some other geometric feature

### Logic

### Geometry

- Conceptual info
- No
- Mnemonic support (AEIO, purpurea ...)
- No
- Form
- none
- Label type
- generic placeholders
- 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
- Yes
- Label type
- linguistic
- Language
- English
- Contains partial sentences or single words
- Yes
- Contain abbreviations
- Yes

### Vertex description

### Edge description

- Diagram is colored
- No
- Diagram is embellished
- No
- Tags
- Leuven ;
- composed operator duality ;
- duality

### Style

### Additional notes

- 'L', 'M' and 'R' stand for left (= external), middle and right (= internal) negation, respectively.