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Johnson solid honeycomb means Convex honeycombs covered with regular Voronoi polygons excluding convex uniform honeycombs.
They are composed of one of Johnson solid at least.
Above all, the combination of Bilunabirotunda, cube and dodecahedron is an only pattern that have regular pentagonal Voronoi polygon.

List of Johnson solid honeycomb

Platon solid	P	Archimedean solid	Johnson solid	J	J	J	Voronoi polygon
			J26 Gyrobifastigium (Digonal gyrobicupola)				(3,4)
			J1 Square pyramid	J3 Triangular cupola			(3,4,6)
			J1 Square pyramid	J27 Triangular orthobicupola			(3,4)
Tetrahedron			J1 Square pyramid				(3,4)
Tetrahedron			J4 Square cupola				(3,4,8)
Tetrahedron			J8 Elongated square pyramid				(3,4)
Tetrahedron			J15 Elongated square bipyramid				(3,4)
Tetrahedron			J28 Square orthobicupola				(3,4)
Octahedron			J3 Triangular cupola				(3,4,6)
Octahedron			J7 Elongated triangular pyramid				(3,4)
Octahedron			J12 Triangular bipyramid				(3)
		Truncated tetrahedron	J12 Triangular bipyramid				(3,6)
		Truncated hexahedron	J1 Square pyramid				(3,4,8)
		Cuboctahedron	J1 Square pyramid				(3,4)
Tetrahedron			J1 Square pyramid	J4 Square cupola			(3,4,8)
Tetrahedron			J1 Square pyramid	J18 Elongated triangular cupola			(3,4,6)
Tetrahedron			J1 Square pyramid	J35 Elongated triangular orthobicupola			(3,4)
Tetrahedron			J1 Square pyramid	J36 Elongated triangular gyrobicupola			(3,4)
Tetrahedron			J28 Square orthobicupola	J29 Square gyrobicupola			(3,4)
Cube			J1 Square pyramid	J3 Triangular cupola			(3,4,6)
Cube	Dodecahedron		J91 Bilunabirotunda				(3,4,5)
Cube		Cuboctahedron	J4 Square cupola				(3,4,8)
Cube		Cuboctahedron	J19 Elongated square cupola				(3,4,8)
			J1 Square pyramid	J7 Elongated triangular pyramid	J14 Elongated triangular bipyramid	J26 Gyrobifastigium (Digonal gyrobicupola)	(3,4)
Tetrahedron	Cube	Cuboctahedron	J37 Elongated square gyrobicupola				(3,4)