Yes, you may faucet and untap Basalt Monolith arbitrarily many instances, alone, with no different profit.

The present textual content of Basalt Monolith’s activated skills is as follows:

{T}: Add {C}{C}{C}.
{3}: Untap Basalt Monolith.

The first skill provides three mana, and the second skill prices three mana of any kind, so you should use the mana produced by the primary skill to activate the second skill. Activating each skills so as leads to the sport returning to the identical actual state it was in earlier than both skill was activated, so you may instantly do the identical factor once more.

The related rule for voluntary infinite loops, rule 726.2a says this:

At any level within the sport, the participant with precedence might counsel a shortcut by describing a sequence of sport selections, for all gamers, that could be legally taken based mostly on the present sport state and the predictable outcomes of the sequence of selections. This sequence could also be a non-repetitive collection of selections, a loop that repeats a specified variety of instances, a number of loops, or nested loops, and will even cross a number of turns. It can’t embody conditional actions, the place the result of a sport occasion determines the following motion a participant takes. The ending level of this sequence have to be a spot the place a participant has precedence, although it needn’t be the participant proposing the shortcut.

Like with any infinite loop, you may announce that you’re activating Basalt Monolith’s first skill after which utilizing the mana to activate the second skill any particular variety of instances.

A 2006 article on the Wizards web site describes some earlier power-level errata to Basalt Monolith that prevented this loop from working:

This card had textbook power-level errata beforehand; it mainly mentioned “you can’t use Basalt Monolith to untap itself.” I’m undecided if this clause was invented to cease combos with Power Artifact or the outdated wording of Relic Bind, however both method it was unhealthy information. It is eliminated, and Power Artifact followers throughout the globe can rejoice!