S^3:         (1, 0, 0, 1)
RP^3:        (1, 0 + Z_2, 0, 1)
L_3_1:       (1, 0 + Z_3, 0, 1)
L_4_1:       (1, 0 + Z_4, 0, 1)
L_5_1:       (1, 0 + Z_5, 0, 1)
L_5_2:       (1, 0 + Z_5, 0, 1)
L_6_1:       (1, 0 + Z_6, 0, 1)
L_7_1:       (1, 0 + Z_7, 0, 1)
L_7_2:       (1, 0 + Z_7, 0, 1)
L_8_1:       (1, 0 + Z_8, 0, 1)
L_8_3:       (1, 0 + Z_8, 0, 1)
L_9_1:       (1, 0 + Z_9, 0, 1)
L_9_2:       (1, 0 + Z_9, 0, 1)
L_10_1:      (1, 0 + Z_10, 0, 1)
L_10_3:      (1, 0 + Z_10, 0, 1)
cube_space:  (1, 0 + Z_2^2, 0, 1)
P_3:         (1, 0 + Z_4, 0, 1)
P_4:         (1, 0 + Z_2^2, 0, 1)
P_5:         (1, 0 + Z_4, 0, 1)
P_6:         (1, 0 + Z_2^2, 0, 1)
P_7:         (1, 0 + Z_4, 0, 1)
P_8:         (1, 0 + Z_2^2, 0, 1)
P_9:         (1, 0 + Z_4, 0, 1)
P_10:        (1, 0 + Z_2^2, 0, 1)
octahedron_space:      (1, 0 + Z_3, 0, 1)
truncated_cube_space:  (1, 0 + Z_2, 0, 1)
Poincare_sphere:       (1, 0, 0, 1)