Income taxes - Additional Information (Detail) - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2023	Dec. 31, 2022	Dec. 31, 2021	Dec. 31, 2017
Income Tax Disclosure [Line Items]
Dividends received from Kronos Worldwide, Inc.	$ 26,766	$ 26,766	$ 25,356
Deferred Tax Assets, Operating Loss Carryforwards	11,800
Gross unrecognized tax benefits	7,300	7,300	7,300
Uncertain tax position	3,707	2,714
Unrecognized tax benefits, if recognize which would affect effective tax rate	7,300
Currently payable	307	495	26
Payables to affiliates	634	665
Noncurrent payable to affiliate	5,074	4,279
Federal Income Tax Purposes
Income Tax Disclosure [Line Items]
Net operating loss carryforwards	$ 3,600
Net operating loss carryforwards expiration description	an indefinite carryforward period subject to an 80% annual usage limitation.
Kronos
Income Tax Disclosure [Line Items]
Dividends received from Kronos Worldwide, Inc.	$ 26,800	26,800	$ 25,400
Deferred income tax asset valuation allowance	0
Deferred Tax Assets	3,500	$ 900
Non-cash deferred income tax expense	2,600
Unpaid transition tax payable	33,500
Kronos | Related Party | Valhi
Income Tax Disclosure [Line Items]
Payables to affiliates	14,900
Noncurrent payable to affiliate	$ 18,600
Kronos | Canada
Income Tax Disclosure [Line Items]
Operating loss carryforwards expiration period	20 years
Kronos | Deferred Tax Liability Non Current
Income Tax Disclosure [Line Items]
Uncertain tax position	$ 3,600
Kronos | Corporate Tax Purposes | German
Income Tax Disclosure [Line Items]
Operating Loss Carryforwards	478,700
Deferred Tax Assets, Operating Loss Carryforwards	75,800
Kronos | Corporate Tax Purposes | Belgium
Income Tax Disclosure [Line Items]
Operating Loss Carryforwards	47,000
Kronos | Corporate Tax Purposes | Canada
Income Tax Disclosure [Line Items]
Operating Loss Carryforwards	31,500
Deferred Tax Assets, Operating Loss Carryforwards	4,700
Kronos | Trade Tax Purposes | German
Income Tax Disclosure [Line Items]
Operating Loss Carryforwards	54,500
Deferred Tax Assets, Operating Loss Carryforwards	5,900
Kronos | Provincial Tax Purposes | Canada
Income Tax Disclosure [Line Items]
Operating Loss Carryforwards	34,900
Deferred Tax Assets, Operating Loss Carryforwards	$ 4,000
Kronos European Subsidiaries | Transition Tax
Income Tax Disclosure [Line Items]
Currently payable				$ 74,500
Current income tax expense payment period				8 years