Listener Crossword 4162: Solution Notes

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Carte Blanche with a Twist by Mash

Puzzle explanation

The initial infinitely repeating grid could be seen alternatively as the surface of a torus, with opposite edges considered to join up. The final grid similarly represents the surface of a Klein bottle, where the top and bottom edges are joined up in reverse. The grid is supposed to be transparent, with the entries from the bottom half of the first grid (shown in blue here) written on the “back” and therefore visible in reverse. Letters from the back either show through the initial gaps or are symmetrical and coincide with the letters from the front, except for an S in the bottom row, which is combined with its reverse to form an 8 in the eighth column of the submission grid. Reading the eighth non-space character of each clue spells out “fundamental polygon”, a term for a diagram such as the final grid that represents a continuous surface, and “4th dimension”, without which it is not possible to construct a non-intersecting Klein bottle. The diagonal phrase KLEIN BOTTLE (with the first L and last E reversed) was to be highlighted.

Clue explanations

Conventions: * = anagram, < = reversal

No Answer Explanation
ACROSS
1 KAMASUTRA (TRAUMA ASK) *
3 FIRMAMENT FIRM + MEANT with A at front
4 CONTUMELY NUT * in COMELY
7 BICIPITAL homophone of BUY + CAPITAL with I for A
8 BOTTOMS UP BOTTOM’S UP
10 AUTOMATIC AU + TOMAT(o) + I’ + C(hef)
12 MULTIMODE (EMIT + M + LOUD) *
13 CARTESIAN CARTES + IAN
16 LITIGIOUS LIT + GI in IOUS
17 WHITEHEAD WHITE HEAD
19 AMAUROSIS (SAMURAI SO) *
21 DOOMSTERS DOERS around MOST *
22 THOUSANDS THOU + SANDS
25 SUBATOMIC SUB, ATOMIC
26 NABATAEAN (NB + TEN) with A inserted alternately
DOWN
1 WHISKY MAC SKY in (WHIM + AC)
2 THUMB KNOT THUMB + KNOT
5 COLUMBATE COLUMBUS with ATE for US
6 APOCOPATE A + POCO + PATÉ
9 CHEMOSTAT MOST in CHEAT
10 ACUMINATE A + CUMIN + ATE
11 OUTERWEAR near-homophone of OWT AWARE
14 MALVOISIE (OLIVES + (sal)AMI) *
15 MITIGATED (I EDIT T’MAG) *
18 ISODICONS IS + ODI + CON + S
19 METABASIS MET + AB + AS IS
20 MASTODONS (TO + DON) in MASS
23 ANTISERUM E in (ANT IS + RUM)
24 TUMESCENT TUM + (d)ESCENT
27 BEAUTIFUL (BEAU + FUL(l)) around IT <
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