A family of novel compounds with planar tetracoordinate silicon (ptSi) supported by B-heterocyclic carbenes (BHCs) have been theoretically investigated. The lowest energy molecules (a3, b3, and c3) with single ptSi are a triplet. We further designed 1D and 2D compounds with multi-ptSi atoms by condensation of a3 along latitudinal (m) and longitudinal (n) directions. The lowest energy 1D compounds prefer to be zigzag conformation along the m direction. The lowest energy 2D compounds (m,n) (m >= n) are zigzag conformation along both m and n directions. The total spin quantum number (S) of the lowest energy compounds with ptSi is equal to the number of ptSi. Thus, the compounds with ptSi stabilized by BHCs are magnetic. The singly occupied molecular orbitals (SOMOs) of such compounds are mainly the linear combination of the 3p orbitals of ptSi, indicating that the magnetism of the compounds originates from ptSi.