A variant of the usual badge. In this example, an equilateral triangle formed of one red triangle surrounded by three dark blue (cf black) triangles.
Unless a manufacturer's error / variation, there is no clear reason for the blue as opposed to black background colour.
The design of the badge owes nothing to the sign worn by the Division in the First World War – a circle with saltire overlaid, in yellow. The WW2 badge was designed in 1940 by the Divisional commander at the time, the then Maj. Gen. B. L. Montgomery, with his AQ. His intention was just “to indicate the combination of threes” – 3rd Division, three brigades and three battalions in each brigade. One might add the three field Artillery regiments and three Engineer companies and one of the Division's historians was at pains to point out that the black brigade triangles must also be seen to include such associated supporting arms.
Another explanation often used, and displaying the British soldier’s famous gallows humour, is that the three black triangles represent the brigades and the red is blood. More abstractly, it might be argued that the red portion represents the command element at the core of the Division. One heartfelt explanation once offered by a harassed adjutant was that the Brigades were bound together by red tape.
The Division won the title of "the Ironsides" or "The Iron Division" in WWI and this carried forward into WWII, especially following an address by Montgomery to his troops after taking command.
It was known during the NWE campaign as 3rd (British) Division to differentiate it from the 3rd (Canadian) Division, also in 21 A. Gp. and for the assault and consolidation phase, also in 2 Army.
A Regular Division in the UK at the outbreak of war the Division fought with the BEF in the 1940 campaign in France and Belgium. It remained thereafter in the UK and in June 1942 was reorganized as a Mixed Division (ie: with one armoured and two infantry brigades – 8 & 9 Infantry and 33 Tank Bdes.). In April 1943 it reverted to an Infantry Division. It was selected for the assault wave of the invasion of NW Europe and landed as the left flank division around Ouistreham on D Day. It fought throughout the NWE campaign to the end of the war in Europe.
Immediately after the War the Division was sent to Palestine, HQ arriving in Jerusalem in November 1945. After a spell in the Canal Zone the Division returned to Palestine in April 1946 where it was disbanded in June 1947.
The Division was reformed in the UK in November 1951, and after tours in the Canal Zone and Cyprus it returned to the UK in July 1954. It formed part of the follow-up forces for the Suez Operation, Operation Musketeer, in 1956. It returned to Cyprus in June 1958.