  We study the shape of sunspot cycles using the Wolf sunspot numbers and group
sunspot numbers of solar cycles 1-23. We determine the most typical "model"
cycles and the most asymmetric cycles, and test the validity of the two
Waldmeier rules: the anti-correlation between cycle height and the length of
its ascending phase (rule 1), and between cycle height and the length of the
preceding cycle (rule 2). We applied the principal component analysis to
sunspot cycles and studied the first two components, which describe the average
cycle shape and cycle asymmetry, respectively. We also calculated their
autocorrelation in order to study their recurrence properties. The best model
cycles for Wolf numbers are SC12, SC14, and SC16, the successive even cycles
from a long period of rather low overall solar activity. We find that the model
cycles in eight different analyses using both sunspot series are almost
exclusively even cycles. Correspondingly, the most asymmetric cycles are odd
cycles. We find that both Waldmeier rules are valid for the whole Wolf number
series of 23 cycles. Waldmeier rule 2 is also valid for group number series
although its significance is weaker. Waldmeier rule 1 is not significant for
the original group number series, but becomes significant for the proxy series.
For separate centuries, Waldmeier rules are not always valid for Wolf numbers
and very rarely for group numbers. Our results also offer a new interpretation
for the Gnevyshev gap. In addition to being a local depression of solar
activity, the Gnevyshev gap is a separatrix that divides cycles into two parts
whose relative intensities determine the cycle asymmetry. The Gnevyshev gap is
the zero value time of PC2, located approximately 33-42% into the cycle after
its start.
