System for constructing a module of a building, comprising: • A plurality of core construction elements which each comprise, in cross section, a cross comprising two main arms of equal length, the main arms intersecting at right angles at mid-length, each core construction element having a plane of symmetry about the axes of each main arm , • A plurality of construction elements for surrounding the core elements , each surrounding element being composed of four partially surrounding parts which are assembled around a core element , • The partially surrounding parts each have a section which is substantially an isosceles-rectangular triangle comprising a long side and two inclined sides which form a right angle, the four partially surrounding parts , once assembled, are arranged with their long side on the outside and the inclined sides terminating at the right angle on the inside toward the center of the cross of a core element , thus forming a square which surrounds the cross of the core element , • the main arms of the cross of each core construction element terminating, at their ends, in transverse parts of which the length is less than the length of the main arms , and • the triangular partially surrounding parts of the surrounding construction elements comprising openings which surround the main arms and the transverse parts of the cross of the core element characterized in that: • the surrounding elements are each composed of four triangular-shaped partially surrounding parts which each have openings within each triangular partially surrounding part in the form of a main arm of the cross extending from the right angle of the triangle with its transverse projections facing the long side of the triangle in such a way that the main arms of the cross and any T-shaped parts are parallel to the sides of the square which is formed by the four assembled partially surrounding parts . • A plurality of core construction elements which each comprise, in cross section, a cross comprising two main arms of equal length, the main arms intersecting at right angles at mid-length, each core construction element having a plane of symmetry about the axes of each main arm , • A plurality of construction elements for surrounding the core elements , each surrounding element being composed of four partially surrounding parts which are assembled around a core element , • The partially surrounding parts each have a section which is substantially an isosceles-rectangular triangle comprising a long side and two inclined sides which form a right angle, the four partially surrounding parts , once assembled, are arranged with their long side on the outside and the inclined sides terminating at the right angle on the inside toward the center of the cross of a core element , thus forming a square which surrounds the cross of the core element , • the main arms of the cross of each core construction element terminating, at their ends, in transverse parts of which the length is less than the length of the main arms , and • the triangular partially surrounding parts of the surrounding construction elements comprising openings which surround the main arms and the transverse parts of the cross of the core element characterized in that: • the surrounding elements are each composed of four triangular-shaped partially surrounding parts which each have openings within each triangular partially surrounding part in the form of a main arm of the cross extending from the right angle of the triangle with its transverse projections facing the long side of the triangle in such a way that the main arms of the cross and any T-shaped parts are parallel to the sides of the square which is formed by the four assembled partially surrounding parts . <EOS>