  Sparse arrays can resolve significantly more scatterers or sources than
sensor by utilizing the co-array - a virtual array structure consisting of
pairwise differences or sums of sensor positions. Although several sparse array
configurations have been developed for passive sensing applications, far fewer
active array designs exist. In active sensing, the sum co-array is typically
more relevant than the difference co-array, especially when the scatterers are
fully coherent. This paper proposes a general symmetric array configuration
suitable for both active and passive sensing. We first derive necessary and
sufficient conditions for the sum and difference co-array of this array to be
contiguous. We then study two specific instances based on the Nested array and
the Kl{\o}ve-Mossige basis, respectively. In particular, we establish the
relationship between the minimum-redundancy solutions of the two resulting
symmetric array configurations, and the previously proposed Concatenated Nested
Array (CNA) and Kl{\o}ve Array (KA). Both the CNA and KA have closed-form
expressions for the sensor positions, which means that they can be easily
generated for any desired array size. The two array structures also achieve low
redundancy, and a contiguous sum and difference co-array, which allows
resolving vastly more scatterers or sources than sensors
