The antenna might look like this:

The W2PM Mini Diamond Flag.
My NEC-2 analysis shows that it has:
Z = 670 + j51.3 SWR (800) = 1.21
RDF = 7.91
Gain = -43.5 dB
Takeoff = 36 deg. on 3.52 MHz with h=1 m (3.1 ft) above an average ground.
These data are quite impressive, taking into account that this antenna is extremely small (the same size as many others building "magnetic" loops). The low gain (read high attenuation) can be a problem - there is high demand on the transformer and common mode currents suppression, also a 30 dB amplifier is a must. Anyway, the radiating pattern looking very nice:

The vertical radiation pattern. The takeoff angle is some 36 degrees.

The horizontal radiation pattern. Note the nice cardioid with excellent F/B.

The 3D radiation pattern of the W2PM Mini Diamond Flag.
The SWR response is flat from 1.8 to 4 MHz. A 1:16 transformer is used for impedance matching to a 50 ohm coax.

SWR Response 1.8 - 4 MHz

Smith chart
The figures above are valid with a 1:16 transformer wound on 3 stacked BN73-202 binocular cores (glued together) with 2 turns on primary (coax side) and 8 turns secondary (antenna side). A detailed transformer description is here.
Here are some photos takem from Pete's archive:

Front view of the W2PM Mini Diamond Receiving Flag

Another view of the W2PM Mini Diamond Receiving Flag

The transformer

... and the terminating resistor






