The characteristic or quality of being grimy(noun)
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Use "griminess" in a sentence
"So maybe it is something else completely different, or just the plain old griminess politicians do."
"They had to be made of dark fabrics with broken patterns to conceal their griminess."
"Altogether the dilapidated condition of the University buildings, the gloominess of the corridors, the griminess of the walls, the lack of light, the dejected aspect of the steps, the hat-stands and the benches, take"