"""Programmatic construction for Book XII, Proposition 5 (XII.5).
Two pyramids ABCG and DEFH of the same height with triangular bases ABC and
DEF and vertices G and H, each divided into two pyramids and two prisms, and
solid magnitude W.
"""
from __future__ import annotations
from geometor.model import Model
def construct_g1() -> Model:
"""Construct the figure 0390.g1 using geometor.model."""
model = Model("XII.5")
# Left pyramid ABCG
G = model.set_point(95.0, -24.0, classes=["given"], ID="G")
A = model.set_point(23.0, -192.0, classes=["given"], ID="A")
B = model.set_point(88.0, -232.0, classes=["given"], ID="B")
C = model.set_point(178.0, -192.0, classes=["given"], ID="C")
K = model.set_point(55.5, -212.0, ID="K")
O = model.set_point(133.0, -212.0, ID="O")
L = model.set_point(100.5, -192.0, ID="L")
P = model.set_point(66.2, -91.2, ID="P")
M = model.set_point(92.2, -107.2, ID="M")
N = model.set_point(128.2, -91.2, ID="N")
# Solid W parallelepiped vertices and label center
W1 = model.set_point(164.0, -22.0, ID="W1")
W2 = model.set_point(292.0, -22.0, ID="W2")
W3 = model.set_point(292.0, -98.0, ID="W3")
W4 = model.set_point(164.0, -98.0, ID="W4")
W5 = model.set_point(185.0, -54.0, ID="W5")
W6 = model.set_point(313.0, -54.0, ID="W6")
W7 = model.set_point(313.0, -130.0, ID="W7")
W8 = model.set_point(185.0, -130.0, ID="W8")
W = model.set_point(238.5, -76.0, classes=["given"], ID="W")
# Right pyramid DEFH
H = model.set_point(437.0, -24.0, classes=["given"], ID="H")
D = model.set_point(286.0, -192.0, classes=["given"], ID="D")
E = model.set_point(364.0, -232.0, classes=["given"], ID="E")
F = model.set_point(494.0, -192.0, classes=["given"], ID="F")
Q = model.set_point(325.0, -212.0, ID="Q")
V = model.set_point(429.0, -212.0, ID="V")
R = model.set_point(390.0, -192.0, ID="R")
S = model.set_point(376.6, -91.2, ID="S")
T = model.set_point(407.8, -107.2, ID="T")
U = model.set_point(459.8, -91.2, ID="U")
# Left segments
for p1, p2 in [
(G, A), (G, P), (P, A),
(G, B), (G, M), (M, B),
(G, C), (G, N), (N, C),
(A, B), (A, K), (K, B),
(B, C), (B, O), (O, C),
(C, A), (C, L), (L, A),
(P, M), (M, N), (N, P),
(K, L), (L, O),
(P, K), (P, L), (M, O),
]:
model.set_segment(p1, p2)
# Solid W segments
for p1, p2 in [
(W1, W2), (W2, W3), (W3, W4), (W4, W1),
(W5, W6), (W6, W7), (W7, W8), (W8, W5),
(W1, W5), (W2, W6), (W3, W7), (W4, W8),
]:
model.set_segment(p1, p2)
# Right segments
for p1, p2 in [
(H, D), (H, S), (S, D),
(H, E), (H, T), (T, E),
(H, F), (H, U), (U, F),
(D, E), (D, Q), (Q, E),
(E, F), (E, V), (V, F),
(F, D), (F, R), (R, D),
(S, T), (T, U), (U, S),
(Q, R), (R, V),
(S, Q), (S, R), (T, V),
]:
model.set_segment(p1, p2)
# Polygons
for poly in [
[A, B, C], [L, O, C], [P, M, N], [K, B, O, L],
[D, E, F], [R, V, F], [S, T, U], [Q, E, V, R],
[W1, W2, W6, W7, W8, W4],
]:
model.set_polygon(poly)
return model
if __name__ == "__main__":
construct_g1()
