The Turan Number of the Triangular Pyramid of $3$-Layers

The Turan number of a graph $H$, denoted by $text{ex}(n, H)$, is the maximum number of edges in an $n$-vertex graph that does not have $H$ as a subgraph. Let $TP_k$ be the triangular pyramid of $k$-layers. In this paper, we determine that $text{ex}(n,TP_3)= frac{1}{4}n^2+n+o(n)$ and pose a conjecture for $text{ex}(n,TP_4)$.