This paper presents a novel method to obtain fully analytical expressions of the magnetic field created by a pyramidal-frustum shaped permanent magnet. Conventional analytical tools only provide expressions for cuboidal permanent magnets and this paper extends these tools to more complex shapes. A novel analytical model for the magnetic field induced by triangular charged surfaces is combined with the field expressions for rectangular charged surfaces. This provides a fully analytical expression for the magnetic field of a pyramidal-frustum shaped permanent magnet. Field and force obtained using this model are validated with Finite Element Modeling.