  The paper concerns Weyl-Heisenberg covariant SIC-POVMs (symmetric
informationally complete positive operator valued measures) and full sets of
MUBs (mutually unbiased bases) in prime dimension. When represented as vectors
in generalized Bloch space a SIC-POVM forms a d^2-1 dimensional regular simplex
(d being the Hilbert space dimension). By contrast, the generalized Bloch
vectors representing a full set of MUBs form d+1 mutually orthogonal d-1
dimensional regular simplices. In this paper we show that, in the
Weyl-Heisenberg case, there are some simple geometrical relationships between
the single SIC-POVM simplex and the d+1 MUB simplices. We go on to give
geometrical interpretations of the minimum uncertainty states introduced by
Wootters and Sussman, and by Appleby, Dang and Fuchs, and of the fiduciality
condition given by Appleby, Dang and Fuchs.
