I think that the Japanese (JNR and its predecessors) EF55 class electric locomotive falls into the unusual category.
It was a double-cab bidirectional locomotive, streamlined at one end but blunt at the other, Cape gauge. The wheel arrangement was 2-C+C-1, with the four-wheel guiding truck at the streamlined, or “fast” end.
Asymmetrical wheel arrangements in and of themselves were not so unusual, and in the field of electric locomotives there were for example 2-C-1, 2-D-1 and C-B locomotives to be found. However, the EF55 was the only 2-C+C-1 example. Three were built in 1936.
One may speculate as to how JNR, etc. arrived at this design. In 1923 it had received some 2-C+C-2 passenger locomotives from English Electric (UK), the first anywhere of this wheel arrangement, these becoming the EF50 class. Then in 1926 it received some 1-C+C-1 locomotives from Westinghouse, also for passenger service, these becoming the EF51 class. Apparently based upon its experience with these, JNR chose the 2-C+C-2 wheel arrangement for its future passenger locomotives, and 1-C+C-1 for its future freight locomotives, which operated at lower top speeds. That was I think consistent with the worldwide experience, which was that articulated-truck locomotives, for example of the C+C type, tended to be rough riding and hard on the track. These tendencies could be tamed somewhat by adding two-wheel pilot trucks, but four-wheel pilot trucks were better for the higher speeds. (For the highest speeds, the addition of a lateral restraint device for the main trucks and possibly lateral restraints for the pilot trucks was considered desirable.)
In the 1930s, the JNR 2-C+C-2 locomotives were all of the non-streamlined, bidirectional boxcab type. Evidently JNR wanted a streamlined locomotive for some of its passenger services. Streamlining with some form of nose end was better done at one end only if there was a requirement that visually, the locomotive should blend in with the trains that it hauled, meaning that the rear end should be more-or-less vertical. Whilst the blunt rear end had a driving cab, presumably for lower-speed manoevering purposes, out on the line, at higher speeds, it would have operated only with the streamlined end forward. That being the case, it was seen that whilst the front end required a 2-C truck, a 1-C truck (of the type used for freight locomotives) would suffice for the trailing end. From that one might infer that JNR thought that the extra stability conferred by the four-wheel pilot truck was required at the front end, but was less important at the rear end.
Be that as it may, JNR did not acquire any more of the EF55 type. Perhaps the 2-C+C-1 wheel arrangement did not work as well as expected, or perhaps what was effectively a single-ended locomotive was found to be operationally awkward in an environment where the bidirectional type was the norm. Rather it continued to build both the 2-C+C-2 and 1-C+C-1 types, periodically updated, through to 1958, eventually amassing 237 of the former and 297 of the latter. (Worldwide majority numbers in both cases.) The later post-WWII 2-C+C-2 types had semi-streamlined boxcab bodies.
Electrically all of these locomotives, including the EF55, were quite normal, that is working from a 1500 volts DC supply with resistance and motor-grouping control, and without any form of electric braking. So the unusual nature of the EF55 was confined to its appearance and its wheel arrangement.
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