Total number of sigma and pi bonds in tricyclometaphosphoric acid (HPO3)3 is 18.

Tricyclometaphosphoric acid is an inorganic compound with the chemical formula (HPO3)3. It consists of three phosphate groups (PO3) connected to a central phosphorus atom (P). To determine the total number of sigma and pi bonds in tricyclometaphosphoric acid, we need to analyze the bonding between the atoms.

Structure of tricyclometaphosphoric acid:
- Tricyclometaphosphoric acid consists of a cyclic structure with three phosphate groups attached to a central phosphorus atom.
- Each phosphate group (PO3) contains one phosphorus atom (P) bonded to three oxygen atoms (O) through single bonds.
- The central phosphorus atom is bonded to three phosphate groups through single bonds.

Sigma bonds:
- Sigma (σ) bonds are formed by the head-on overlap of atomic orbitals.
- Each single bond between the phosphorus atom and oxygen atoms in the phosphate groups represents a sigma bond.
- Since each phosphate group has one P-O bond, and there are three phosphate groups in tricyclometaphosphoric acid, the total number of sigma bonds is 3 * 1 = 3.

Pi bonds:
- Pi (π) bonds are formed by the sideways overlap of atomic orbitals.
- In tricyclometaphosphoric acid, there are no pi bonds between the phosphorus atom and oxygen atoms in the phosphate groups.
- However, there are pi bonds within each phosphate group due to the resonance structure of the phosphate ion (PO4)3-. Each phosphate group contains one pi bond.
- Since there are three phosphate groups in tricyclometaphosphoric acid, the total number of pi bonds is 3 * 1 = 3.

Total number of sigma and pi bonds:
- The total number of sigma bonds is 3.
- The total number of pi bonds is 3.
- Therefore, the total number of sigma and pi bonds in tricyclometaphosphoric acid is 3 + 3 = 6.

Therefore, the correct answer is not 18, but 6.