This paper explores the quantum dynamics of triangular billiards, classifying them as integrable, pseudo-integrable, or non-integrable based on their internal angles. The authors use five properties—level spacing ratio (LSR), spectral complexity (SC), Lanczos coefficient variance, energy eigenstate localization in the Krylov basis, and dynamical growth of spread complexity—to characterize these systems. Key findings include: 1. **LSR and Spectral Complexity**: Integrable triangles have the lowest LSRs, indicating high level spacing fluctuations. Degeneracies in their spectrum lead to quadratic late-time spectral complexity growth. Pseudo-integrable and non-integrable triangles show slower growth, approaching Poisson and GOE statistics, respectively. 2. **Lanczos Coefficient Variance**: Integrable triangles have the highest Lanczos coefficient variance, followed by isosceles triangles, right triangles, and generic pseudo-integrable and non-integrable triangles. This variance is inversely related to the LSR, suggesting a connection between spectral and dynamical properties. 3. **Energy Eigenstate Localization**: Integrable triangles exhibit the strongest localization of energy eigenstates in the Krylov basis, followed by isosceles triangles, right triangles, and generic pseudo-integrable and non-integrable triangles. 4. **Spread Complexity**: Integrable triangles show a peak in spread complexity followed by a plateau, indicating Poincaré recurrences. Pseudo-integrable and non-integrable triangles exhibit chaotic behavior with an initial rise, followed by a slope down to a plateau. The study also highlights the impact of symmetry on the dynamics, with isosceles triangles showing both chaotic and integrable features in their individual sectors. The authors conclude by discussing future directions, including higher precision numerical analyses and extending these methods to quantum field theories and holography.This paper explores the quantum dynamics of triangular billiards, classifying them as integrable, pseudo-integrable, or non-integrable based on their internal angles. The authors use five properties—level spacing ratio (LSR), spectral complexity (SC), Lanczos coefficient variance, energy eigenstate localization in the Krylov basis, and dynamical growth of spread complexity—to characterize these systems. Key findings include: 1. **LSR and Spectral Complexity**: Integrable triangles have the lowest LSRs, indicating high level spacing fluctuations. Degeneracies in their spectrum lead to quadratic late-time spectral complexity growth. Pseudo-integrable and non-integrable triangles show slower growth, approaching Poisson and GOE statistics, respectively. 2. **Lanczos Coefficient Variance**: Integrable triangles have the highest Lanczos coefficient variance, followed by isosceles triangles, right triangles, and generic pseudo-integrable and non-integrable triangles. This variance is inversely related to the LSR, suggesting a connection between spectral and dynamical properties. 3. **Energy Eigenstate Localization**: Integrable triangles exhibit the strongest localization of energy eigenstates in the Krylov basis, followed by isosceles triangles, right triangles, and generic pseudo-integrable and non-integrable triangles. 4. **Spread Complexity**: Integrable triangles show a peak in spread complexity followed by a plateau, indicating Poincaré recurrences. Pseudo-integrable and non-integrable triangles exhibit chaotic behavior with an initial rise, followed by a slope down to a plateau. The study also highlights the impact of symmetry on the dynamics, with isosceles triangles showing both chaotic and integrable features in their individual sectors. The authors conclude by discussing future directions, including higher precision numerical analyses and extending these methods to quantum field theories and holography.