I wanted to get rid of that stupid blinking "Under Construction" in first place. Therefore I decided to write at least something useful at this place. Hope you all agree.

Let's start with some CPU-basics.

It helps if you can read. Since you are here (at this place) I think you can. In this case you should study the writing atop the CPU.

Non-MMX Pentium are labelled Intel pentium i200 or i166.
MMX Pentiums are labelled Intel pentium w/ MMX^tm tech

Sometimes you cannot read the writing atop (anymore) or it is blocked by a heatsink, a glued one for instance, a glued heat-spreader or soild with thermal grease goo. In this case look at the underside:

Non-MMX Pentiums are labelled intel pentium FV80502xxx SY045/VSU
MMX-Pentium are labelled intel pentium w/ MMX tech FV80503xxx SL27J / 2.8V

xxx can be 166, 200 or 233 - whatever speed rating they'd used. The SY... indicates a 3.3V processor, the SJ... is a dual-rail MMX, where "2.8V" gives the core voltage for the second (inner) plane. The external interface runs at 3.3V in either case.

MMX CPU usually had the plastic case with the small silver heat spreader - but not always. I have seen a few all-ceramic types with white lettering, but the "MMX tech" is always clearly visible, on top as well as on the underside.
That should suffice to differ the two.

Warning: Never try to install a Pentium MMX CPU on the P90 platform directly !

Its processor core runs at a lower voltage and it gets overheated and ruined before your system has finished POST most likely. For the MMX types you need a special adapter with a secondary power regulator, which reduces the core voltage to an appropriate level. One of these adapters is the Madex 486007 adapter. It consists of two parts: 1. the socket adapter for the CPU itself and 2. an external switchmode regulator, which is directly connected to the main power supply to put out the required 3.5 - 4.5 Amps at 2.8V for the MMX CPU core.

They are connected with two 4-pin plugs (blue cables) and the regulator is connected with another 4-pin 3.5" FDD-style DC-plug to the main power supply. The regulator has 4x DIL-switch (right from the heatsink) and can be programmed to the corresponding core voltage. The large golden heatsink and a fixing clip - unfortunately for a wider Socket-7 board only - could be ordered separately and were not part of the base kit itself.

The socket part needs to be carefully installed on the platform socket. It has very thin pins that go into the CPU socket. These pins tend to bend and break very easy and that will ruin the party. Not all pins go into the socket however: these that carry the lower core voltage are fed to the CPU from that intermediate printboard visible in the picture. No need to route pins further down.

Once you'd installed adapter socket, CPU, regulator and CPU heatsink the system should come up as normal. There are jumpers on the adapter socket to set the matching BF0 / BF1 signalling for the core / bus ratio. On the 60 MHz (unmodified) platform a 1:3 ratio will bring you to 180 MHz. For a testrun I would suggest to leave the pins open and try out the combo at the usual 90 MHz processor speed. Then "work your way upwards" if CPU and platform are capable to run at 210 MHz as well with a 1:3.5 ratio.

Back then, when I collected a lot stuff for Pentium-1 CPUs I once bought this MMX adapter / regulator module along with a mainboard (Non-IBM).
This thing is typical for the silly simple approaches people tried to "make fit" MMX-CPUs on Socket-7 Non-MMX-ready platforms. It consists of an interposer board that takes off the secondary core voltage from the 3.3-Volt plane and adds jumpers for setting the new core voltage and the bus / core clock ratio.
For this purpose it has another member of the LT-108x-regulator family onboard and gets the power from the main power supply via a male-female device DC-plug, which got a 4-pin 3.5"-FDD-like plug as well to feed the module.
At least this prevents the onboard 3.3V regulator from getting overloaded.
However: the whole design is a tad awkward as you can see from the pictures below.

View onto DC-input and the jumpers ...	... and how the fixing runs around the edge.
View from the MCA side upwards	LT-style regulator with own heatsink

The problem here is, that the jumpers line up along the one side where a clip, clamp or "whatever method" to keep the heatsink on the CPU should go. My construction is silver wires, tooled along the lower socket hooks and strapped together inside the heatsink with a nylon cable tie. Usually this works quite good, but on this adapter the holding wires run around the edge of the interposer board and - well - barely fit inside the lower hook. Additionally this asymmetry pulls the heatsink off-center and I were a bit concerned on the reliablilty if I would plan to run this thing for longer.
(Which I don't to be honest)

Take this as a "Technology Demonstration": the platform I'd tried it onto flat out refused to properly boot with this combo. It complains about a platform change as usual, but during the refdisk load it dumps into a 0129 1500 error. I'm not 100-percent sure, but I think the MMX processor I'd used had been running in a clone board with a 3.3V-core voltage for some time ... instead of 2.8V as required. I might have accidentially picked it.

Whatever: from the principle it should work and you might get a similar looking result if you manage to find one of those regulator-adapters.
Properly and reliably fixing the heatsink might be your biggest challenge.