S^3:         (5,10,10,5)      <-- vertex-minimal
RP^3:        (11,51,80,40)    <-- vertex-minimal
L_3_1:       (12,66,108,54)   <-- vertex-minimal
L_4_1:       (14,84,140,70)
L_5_1:       (15,97,164,82)
L_5_2:       (14,86,144,72)
L_6_1:       (16,110,188,94)
L_7_1:       (17,123,212,106)
L_7_2:       (16,104,176,88)
L_8_1:       (17,130,226,113)
L_8_3:       (16,106,180,90)
L_9_1:       (18,143,250,125)
L_9_2:       (16,114,196,98)
L_10_1:      (19,155,272,136)
L_10_3:      (17,118,202,101)
cube_space:  (15,90,150,75)
P_3:         (15,97,164,82)
P_4:         (15,104,178,89)
P_5:         (17,122,210,105)
P_6:         (17,130,226,113)
P_7:         (18,143,250,125)
P_8:         (19,155,272,136)
P_9:         (19,163,288,144)
P_10:        (20,175,310,155)
octahedron_space:      (15,102,174,87)
truncated_cube_space:  (16,109,186,93)
Poincare_sphere:       (16,106,180,90)