Superprismane is a porous, three-dimensional carbon allotrope that combines super-hardness, ductility and low effective-mass charge carriers attributes that make it promising for blue-to-UV optoelectronics and high performance structural applications. In this work, we employ the M-polynomial framework to extract complete closed-form expressions for seven classical Zagreb-type topological indices and their seven multiplicative counterparts for an arbitrary \(p\times k\) superprismane lattice. Three-dimensional index surfaces are visualized and benchmarked against two canonical carbon networks \({6.8}^{2}\;\text{D}\) and graphite. Using least-squares regression, we demonstrate that the multiplicative inverse-sum index achieves a perfect correlation ( \(r=1.00\) ) with shear modulus and an almost perfect correlation ( \(r=0.99\) ) with Young’s modulus, outperforming all other descriptors. These results show that M-polynomial-derived indices provide a rapid, inexpensive alternative to density-functional calculations for predicting bulk mechanical properties, enabling high-throughput computational screening of novel carbon materials. The study closes a gap in the literature by delivering the first comprehensive suite of additive and multiplicative indices for a three-dimensional porous carbon network and establishes a foundation for data-driven design of advanced allotropes.
