There really is no specific antenna design that answers to the name "Double Discone" but some Bicone or Biconical style antennas are marketed for scanner use and sold mostly in the UK and Europe.
A Biconical antenna would resemble two cones of a Discone, one facing up and one facing down and a complex matching network at the feedpoint to keep the impedance constant over several octaves.
I purchased a "Nevada" brand "Double Discone" several years ago and it appears to be nothing special. There is no matching network at the feedpoint and its simply two typical scanner Discone cones stuck onto a coax connector. The antenna covers part of the VHF range with a reasonable match but its not usable for transmitting over a broad range of frequencies like a typical Discone or a properly designed Biconical antenna. Over the year or so I had this antenna up I saw no advantage over a similar size Discone and a serious disadvantage if you need to transmit.
I also have a commercial/military Harris RF-9070 VHF/UHF Biconical for comparison with the Nevada. The Harris is much larger than the Nevada and cost about 20 times as much and the difference in performance is almost as much as the difference in price. The Harris only covers 100-400Mhz with degraded specs at 90-470MHz and the smaller, cheezier Nevada is rated 25-1300MHz.( How does Nevada determine this, with a Ouija board?)
Either the Nevada people are pure antenna genius's and the Harris people don't have a clue, or its the other way around. What do you guys and girls think?
prcguy