On the structure of spikes II

Figures & data

Table

$({\underset{¯}{v}}_1,{\underset{¯}{v}}_2,{\underset{¯}{v}}_3,{\underset{¯}{v}}_4)$	All possible members of $\phi$ under (38)
$(1,0,0,0)$	$\{Z:|Z\cap Y_1|\in {\mathcal{P}}_4,|Z\cap Y_2|\in {\mathcal{P}}_5 \mathit{\text{and}}|Z\cap Y_4|\in {\mathcal{P}}_5\}$
$(0,0,0,2)$	$\{Z:|Z\cap Y_1|\in {\mathcal{P}}_5,|Z\cap Y_2|\in {\mathcal{P}}_5 \mathit{\text{and}}|Z\cap Y_4|\in {\mathcal{P}}_3\}$
$(0,2,0,1)$	$\{Z:|Z\cap Y_1|\in {\mathcal{P}}_5,|Z\cap Y_2|\in {\mathcal{P}}_3 \mathit{\text{and}}|Z\cap Y_4|\in {\mathcal{P}}_4\}$
$(1,1,0,2)$	$\{Z:|Z\cap Y_1|\in {\mathcal{P}}_4,|Z\cap Y_2|\in {\mathcal{P}}_4 \mathit{\text{and}}|Z\cap Y_4|\in {\mathcal{P}}_3\}$
$(1,3,0,1)$	$\{Z:|Z\cap Y_1|\in {\mathcal{P}}_4,|Z\cap Y_2|\in {\mathcal{P}}_2 \mathit{\text{and}}|Z\cap Y_4|\in {\mathcal{P}}_4\}$

Fig. 1 Geometric Representations of the only Six 3-Spikes.

Fig. 2 Illustrating Conjecture 21 to characterize the class ${\mathcal{S}}_r$.