Please, if I messed some factoid up, please correct me and provide the proper facts. Though I do trust Memory Alpha muchly.

Intellectuals

J…A…T…U…

Anticipatory fingers lingering over the PADD touch screen retreated to a light fixture, prompting illumination with the contact. Shoulders squared and legs recrossed, the intense gaze scanned the screen with heightened focus.

J…from P'Jem, without a doubt correct. Vulcan monastery, five letters, he'd seen it used once before, and additionally, it was his territory. The J was solid.

A…from PADD, a popular choice for the letters it provided in a short four letter package. Clue, cptn sign-off…The A was solid.

T…from tricorder, the regular rationalization was scarcely necessary but, naturally, logical. Medical or scientific, nine letters, the second r being a link to z-dimension Tellar, Tellarite home base ____ Prime, six letters. As Tellar's t was borrowed in – a sharp fingertip stroke on the edge of the screen rotated the cube's faces, and a second to the side desired – yes, the t was the first of six letter Axanar ship: Tuk-dak. As this clue was confirmed, Tellar was logically correct and thus the r in tricorder belied the word's necessity. The t, from tricorder, was solid.

Finally U…From quad, unit of measure, four letters, d confirmed by z-dimension dominian, Cardassian system locale. The factual clue dominian was assuredly accurate, and as it's connection to quad was satisfied with the terminating d, the entailed u was solid.

First letter J… fourth letter A… sixth letter T… final letter U, eight letters, clue – "Nyota." Uhura peered into the room with a quizzical expression. "Romulan greeting, starts with a 'J'," she smiled discreetly as she paused her interweb computer game and came to stand behind Spock's armchair.

"Let me see…"

"Twelve, x-dimension." A second pair of dark eyes joined the two at the difficult puzzle juncture.

Romulan greeting; J, blank, blank, A, blank – "Jolan tru," she pronounced after the brief consideration. The anxious fingers returned to the keying panel as arms looped around his shoulders, a hand rested on his chest and a hand guided him through the orthographics. "J, o, l, a, n, t, r, u: Jolan tru."

Spock studied the crossword cube from all six sides before nodding in satisfaction and avidly searching for the few remaining unanswered clues. Uhura's gesturing appendage reposed to rest aside its fellow, joining it in a vigorous rub of the black expanse of toned Vulcan torso. She chuckled behind a grin and kissed the well kept fringe above a delicately pointed ear before smoothly disentangling herself and returning to her virtual alien zapping.

13, y-dimension… Spock looked up abruptly in remembrance. "Nyota." Her inquiring face appeared once more in the doorway. "Thank you for your intellectual contribution."

She smiled warmly at the characteristic attention to "illogical human needs" and replied with professional clarity of voice, "Anytime, baby."