When it comes to describing something that is truly steadfast and immovable, there are many synonyms that could capture the sentiment of "admitting no exception". For example, we might say that the thing in question is absolutely inflexible or unwavering, meaning that there is no possibility of it bending or changing under any circumstances. Alternatively, we could describe it as completely rigid or intractable, implying that it is utterly unyielding and resists any efforts to alter its course. Ultimately, when we say that something admits no exception, we are suggesting that it is completely and utterly fixed in its position, and that there are no circumstances that could cause it to budge even a single inch.