# Re-producing the 3D Connecting Wall!

This puzzle is part of the Monthly Topic Challenge #11: Now in 3D. See Introducing the 3D Connecting Wall! for the original presentation of this puzzle type and further context. This post presents a second 3D Connecting Wall after taking the opportunity to hone the visual and verbal instructions.

The diagram below depicts three adjacent sides of a 4x4x4 cube, each of which is its own 4x4 connecting wall comprising the faces of 16 smaller 'cubelets'. A pool of 37 words must be divided so as to form 12 thematic groups of four. Naturally, this means that - unlike in the 2D connecting wall - in a 3D connecting wall some words must appear in 2 or (in one case) 3 different categories at once! This can best be understood by imagining that each 'cubelet' in the diagram is assigned a word, which is written on each of its visible faces.

The three interconnected connecting walls are labelled T (top), R (right) and L (left), with each category (represented by the subscript numbers 1-4) occupying a run of four cubelet faces in the direction of the guide arrow provided. For example, the elements of category T1 of the top connecting wall are shaded in red and appear along the northwest-southeast diagonal. Each of its elements also appears as an entry in one of categories L1 to L4 (three of which have been shaded pink) - and, in fact, the word to be positioned in the diagram's central cubelet (common to categories T1 and L1) further appears in category R1 also! The word to be placed in the central cubelet is omitted from the list of words provided and must be deduced in order to complete the puzzle.

You are provided with 36 of the 37 words to complete this 3D connecting wall, as follows:

ABOMINABLE ALBERT ANTHONY BEER CASSANDRA CIRCLE
FLEA FLUKE FLYOVER GROAT GUINEA HENRY
JOHN JUBILEE KENYA LUKE MADAGASCAR MARK
MATTHEW MITE MOTHER PASCAL RODNEY TASTING
THATCHER TICK TROLLS TURBO VICTORIA VOLTA

TASK: Position the 36 given words in this 3D connecting wall - one to a cubelet - in order to form 12 thematic groups of size four across the three visible sides of the full cube (in the directions of the given arrows). Discover the hidden word (not provided here) which should be positioned on the diagram's central cubelet, to discover what you see when you unite the blue (R1), yellow (L1) and red (T1) connected groups!

NB The checkmark will be awarded to a correct solution if the following presentational rule is followed: The three elements occupying the unbroken-line portion of each guide arrow (including those for categories shaded in red, blue or yellow) should be arranged in alphabetical order. Two words (TICK and TURBO) have been positioned for you according to this style - the other words should be inserted around them. (With these stipulations, there should only be one way to complete the grid in its entirety...)

• What a very lovely puzzle Aug 3 at 23:46

Completed grid:

Sorry if it's a bit of a mess. I had several false starts in the process.

Top side:

Words starting with an insect: BEER, FLYOVER, MOTHER, ANTHONY
Parasites: FLUKE, MITE, TICK, FLEA
Gospels: LUKE, MARK, MATTHEW, JOHN
African lakes: ALBERT, VICTORIA, VOLTA, CHAD

Left-hand side:

Only Fools and Horses characters: CASSANDRA, DEREK, RODNEY, ALBERT
London tube lines: CIRCLE, DISTRICT, JUBILEE, VICTORIA
Namesake physicists of SI units: FARADAY, HENRY, PASCAL, VOLTA