Was Lewis Carroll an Amazing Oppositional Geometer? (2014), p. 398
by Moretti, Alessio

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Caption

Carroll–Richards' tetrahedron is in fact an oppositional tetrahexahedron.

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

0

Representation of contradiction

By central symmetry

Vertex description

Conceptual info

No

Mnemonic support (AEIO, purpurea ...)

No

Form

dots

Label type

symbolic

Symbolic field

logic

Contains partial formulas or symbols

Yes

Logical system

predicate logic

Edge description

Style

Diagram is colored

Yes

Diagram is embellished

No

Tags

Boolean closed

;

existential import

Additional notes

With the bitstrings based on this partition, the formulas of this diagram (in Greek notation) can be represented as follows:

1000 = $ \alpha\beta\delta $
0100 = $ \alpha\beta\gamma $
0010 = $ \alpha\gamma\delta $
0001 = $ \beta\gamma\delta $
1100 = $ \alpha\beta $
1010 = $ \alpha\delta$
1001 = $ \beta\delta $
0110 = $ \alpha\gamma $
0101 = $ \beta\gamma $
0011 = $ \gamma\delta $
1110 = $ \alpha $
1101 = $ \beta $
1011 = $ \delta $
0111 = $ \gamma $

Note: $\alpha\beta$ means $\alpha\wedge\beta$ (cf. p. 391).