In this paper, we introduce a novel 6-D representation of plenoptic point clouds, enabling joint, non-separable transform coding of plenoptic signals defined along both spatial and angular (viewpoint) dimensions. This 6-D representation, which is built in a global coordinate system, can be used in both multi-camera studio capture and video fly-by capture scenarios, with various viewpoint (camera) arrangements and densities. We show that both the Region-Adaptive Hierarchical Transform (RAHT) and the Graph Fourier Transform (GFT) can be extended to the proposed 6-D representation to enable the non-separable transform coding. Our method is applicable to plenoptic data with either dense or sparse sets of viewpoints, and to complete or incomplete plenoptic data, while the state-of-the-art RAHT-KLT method, which is separable in spatial and angular dimensions, is applicable only to complete plenoptic data. The "complete " plenoptic data refers to data that has, for each spatial point, one colour for every viewpoint (ignoring any occlusions), while "incomplete " data has colours only for the visible surface points at each viewpoint. We demonstrate that the proposed 6-D RAHT and 6-D GFT compression methods are able to outperform the state-of-the-art RAHT-KLT method on 3-D objects with various levels of surface specularity, and captured with different camera arrangements and different degrees of viewpoint sparsity.