First of all, never underestimate the impenetrability of the presidential bubble.
From the time.com
This sense of opacity and impenetrability gives the authorities the upper hand.
From the economist.com
The impenetrability of the plot, and the amorphous cast of characters can be frustrating.
From the chron.com
Indeed, her book seems laced with little self-referential jokes about her own impenetrability.
From the washingtonpost.com
Food writers have struggled to express the ironclad impenetrability of the famous eating-house.
From the independent.co.uk
Impenetrability of image, that old signal of hip-hop authenticity, somehow no longer seems to count.
From the nytimes.com
Architecturally, the impenetrability of today's Capitol complex echoes the Byzantine ways by which bills move toward law.
From the bloomberg.com
As the name suggests, stone is a predominant element on the part of the facade, suggesting some sort of impenetrability.
From the dailyherald.com
The veil of impenetrability has been lifted.
From the washingtonpost.com
More examples
The quality of being impenetrable (by people or light or missiles etc.)
Incomprehensibility by virtue of being too dense to understand
(impenetrable) not admitting of penetration or passage into or through; "an impenetrable fortress"; "impenetrable rain forests"
(impenetrable) dense: permitting little if any light to pass through because of denseness of matter; "dense smoke"; "heavy fog"; "impenetrable gloom"
In metaphysics, impenetrability is the name given to that quality of matter whereby two bodies cannot occupy the same space at the same time. ...
(IMPENETRABLE) Term applied historically to the area of the dry chaco with the most inhospitable conditions for white settlement, due to lack of water; the name of a zone of northwestern Chaco Province.