Long-term debt - Additional Information (Detail) - NLKW Holding, LLC - Valhi - Valhi Credit Facility	3 Months Ended
	Mar. 31, 2024 USD ($)
Debt Instrument [Line Items]
Maximum borrowing under credit facility	$ 50,000,000
Borrowings or repayments under revolving credit facility	0
Outstanding borrowing	500,000
Amount available for future borrowing under revolving credit facility	$ 49,500,000
Debt instrument, description of variable rate basis	prime rate
Variable rate basis spread above reference rate	1.875%
Debt instrument average interest rate	10.38%