Table 3.

Typical Irish tetrahedra

Points	Irish high: 8 symmetries		Irish medial: 3 symmetries		Irish low: 2 symmetries
	Coordinates	Type	Coordinates	Type	Coordinates	Type
Vertices	(−1/4, 1/2, 0)	+	(0, 0, 0)	0	(0, 0, 0)	+
	(1/4, 1/2, 0)	+	(0, 1/4, 1/2)	+	(−1/4, 1/2, 0)	+
	(0, 1/4, 1/2)	+	(1/2, 0, 1/4)	+	(1/4, 1/2, 0)	+
	(0, 3/4, 1/2)	+	(1/4, 1/2, 0)	+	(0, 1/4, 1/2)	+
Node	(0, 1/2, 1/4)	−	(5/24, 5/24, 5/24)	03	(−5/32, 0, 10/32)	−0

Dodecahedral cells have nuclei 0, 1, 2, or 3 and volume 125/1024. Dodecadihedral ones have nuclei + and volume 129/1024. Here 0₃ = (7/12)·0 + (5/12)·3 and −₀ = (5/8)·− + (3/8)·0. Nodes are all points −, 0₁, 1₂, 2₃, 3₀, 0₃, 1₀, 2₁, 3₂, −₀, −₁, −₂, or −₃ with above proportions.