Factor analysis and principal components analysis (PCA) are often foll
owed by an orthomax rotation to rotate a loading matrix to simple stru
cture. The simple structure is usually defined in terms of the simplic
ity of the columns of the loading matrix. In Three-made PCA, rotationa
l freedom of the so called core (a three-way array relating components
for the three different modes) can be used similarly to find a simple
structure of the core. Simple structure of the core can be defined wi
th respect to ail three modes simultaneously, possibly with different
emphases on the different modes. The present paper provides a fully fl
exible approach for orthomax rotation of the core to simple structure
with respect to three modes simultaneously. Computationally, this appr
oach relies on repeated (two-way) orthomax applied to supermatrices co
ntaining the frontal, lateral or horizontal slabs, respectively. The p
rocedure is illustrated by means of a number of exemplary analyses. As
a by-product, application of the Three-mode Orthomax procedures to tw
o-way arrays is shown to reveal interesting relations with and interpr
etations of existing two-way simple structure rotation techniques.