The hexa-transformer is a three-phase transformer with a specially shaped core, arranged in a triangular shape. The core consists of nine rolls of laminated steel bands and the core legs have a cross sectional shape of a hexagonal Transformers built according to this concept are characterised byhigher energy efficiency, lower weight and volume, lower vibrations and noise level, lower electromagnetic stray field, inrush current and lack of third harmonic In addition, compared to the traditional technology of power transformer production that involves a large amount of manual labour, the new technology allows automating the production process to a large extent.
Other than that, they do look very similar to transformers. A coupled inductor would be used, for example, in a flyback converter, where it stores energy while the switch is on, then dumps the energy to the output when the switch is off. Most transformers (other than coupled inductors) are wound on low reluctance cores.
They do have magnetizing and leakage inductances, but these are more like parasitic effects. An ideal transformer does not have these characteristics. An ideal transformer does not store energy.
On the other hand, a coupled inductor is an inductor, and is designed to store a significant amount of energy in the core flux. Because of this, the core has a gap, either a discrete gap or a distributed one, like in a powdered iron core.
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