Developmental Geometry for a Pyramid with an (16 sided) Polygonal Base
Polygonal Trigonometric Functions are to 5 Decimal Places


central angle = 22.5
working angle = 11.25
plan angle = 78.75
miter angle = 2.39 & 12
hip run per foot = 12.2350938984998
apothem multiplier = secant(360 ( N 2 ))
side wall multiplier = tan((360 (N 2 )) 2
apothem_multiplier = 1.01959115820832
side_wall_multiplier = 0.397824734759316
Pitch Radius apothem radius apothem multiplier apothem multiplier * apothem side wall multiplier * apothem Pitch Angle Hip Angle Hip Side Cut Angle Hip Backing Angle Jack Rafter Side Cut Angle Jack Rafter Side Cut Angle 2 Rafter Length Hip Length Span Wall Length Projection Angle A Projection A Projection Angle B Projection B Circumference Freize Block Miter Angle Freize Block Bevel Angle Surface Angle
0.00 48.00000 47.07769 47.07769 48.00000 18.72867 0.00000 0.00000 11.25000 0.00000 11.25000 78.75000 47.07769 48.00000 94.15539 18.72867 22.50000 17.30304 67.50000 7.16715 301.59289 0.00000 11.25000 22.50000
1.00 48.00000 47.07769 47.07769 48.00000 18.72867 4.76364 4.67252 11.21356 0.92831 11.21213 78.78787 47.24087 48.16006 94.15539 18.72867 22.50000 17.30304 67.50000 7.16715 301.59289 0.94637 11.21064 22.42522
2.00 48.00000 47.07769 47.07769 48.00000 18.72867 9.46232 9.28370 11.10633 1.83794 11.10076 78.89924 47.72707 48.63707 94.15539 18.72867 22.50000 17.30304 67.50000 7.16715 301.59289 1.87296 11.09498 22.20529
3.00 48.00000 47.07769 47.07769 48.00000 18.72867 14.03624 13.77691 10.93425 2.71204 10.92230 79.07770 48.52658 49.42185 94.15539 18.72867 22.50000 17.30304 67.50000 7.16715 301.59289 2.76200 10.90992 21.85268
4.00 48.00000 47.07769 47.07769 48.00000 18.72867 18.43495 18.10404 10.70625 3.53699 10.68633 79.31367 49.62425 50.50007 94.15539 18.72867 22.50000 17.30304 67.50000 7.16715 301.59289 3.59926 10.66573 21.38611
5.00 48.00000 47.07769 47.07769 48.00000 18.72867 22.61986 22.22790 10.43304 4.30322 10.40427 79.59573 51.00083 51.85341 94.15539 18.72867 22.50000 17.30304 67.50000 7.16715 301.59289 4.37488 10.37462 20.82795
6.00 48.00000 47.07769 47.07769 48.00000 18.72867 26.56505 26.12299 10.12591 5.00525 10.08809 79.91191 52.63446 53.46099 94.15539 18.72867 22.50000 17.30304 67.50000 7.16715 301.59289 5.08344 10.04922 20.20165
7.00 48.00000 47.07769 47.07769 48.00000 18.72867 30.25644 29.77494 9.79569 5.64131 9.74916 80.25084 54.50202 55.30064 94.15539 18.72867 22.50000 17.30304 67.50000 7.16715 301.59289 5.72342 9.70148 19.52961
8.00 48.00000 47.07769 47.07769 48.00000 18.72867 33.69007 33.17894 9.45207 6.21252 9.39756 80.60244 56.58035 57.35003 94.15539 18.72867 22.50000 17.30304 67.50000 7.16715 301.59289 6.29636 9.34187 18.83172
9.00 48.00000 47.07769 47.07769 48.00000 18.72867 36.86990 36.33779 9.10320 6.72212 9.04166 80.95834 58.84712 59.58753 94.15539 18.72867 22.50000 17.30304 67.50000 7.16715 301.59289 6.80591 8.97899 18.12460
10.00 48.00000 47.07769 47.07769 48.00000 18.72867 39.80557 39.25985 8.75559 7.17462 8.68809 81.31191 61.28142 61.99277 94.15539 18.72867 22.50000 17.30304 67.50000 7.16715 301.59289 7.25702 8.61954 17.42139
11.00 48.00000 47.07769 47.07769 48.00000 18.72867 42.51045 41.95723 8.41418 7.57520 8.34178 81.65822 63.86411 64.54700 94.15539 18.72867 22.50000 17.30304 67.50000 7.16715 301.59289 7.65524 8.26847 16.73199
12.00 48.00000 47.07769 47.07769 48.00000 18.72867 45.00000 44.44422 8.08253 7.92922 8.00626 81.99374 66.57791 67.23324 94.15539 18.72867 22.50000 17.30304 67.50000 7.16715 301.59289 8.00626 7.92922 16.06348
13.00 48.00000 47.07769 47.07769 48.00000 18.72867 47.29061 46.73617 7.76307 8.24192 7.68385 82.31615 69.40745 70.03631 94.15539 18.72867 22.50000 17.30304 67.50000 7.16715 301.59289 8.31555 7.60402 15.42057
14.00 48.00000 47.07769 47.07769 48.00000 18.72867 49.39871 48.84864 7.45730 8.51820 7.37595 82.62405 72.33915 72.94274 94.15539 18.72867 22.50000 17.30304 67.50000 7.16715 301.59289 8.58822 7.29414 14.80613
15.00 48.00000 47.07769 47.07769 48.00000 18.72867 51.34019 50.79681 7.16603 8.76255 7.08324 82.91676 75.36108 75.94066 94.15539 18.72867 22.50000 17.30304 67.50000 7.16715 301.59289 8.82889 7.00015 14.22163
16.00 48.00000 47.07769 47.07769 48.00000 18.72867 53.13010 52.59510 6.88954 8.97899 6.80591 83.19409 78.46282 79.01965 94.15539 18.72867 22.50000 17.30304 67.50000 7.16715 301.59289 9.04166 6.72212 13.66749
17.00 48.00000 47.07769 47.07769 48.00000 18.72867 54.78241 54.25700 6.62775 9.17106 6.54376 83.45624 81.63528 82.17061 94.15539 18.72867 22.50000 17.30304 67.50000 7.16715 301.59289 9.23017 6.45976 13.14339
18.00 48.00000 47.07769 47.07769 48.00000 18.72867 56.30993 55.79498 6.38030 9.34187 6.29636 83.70364 84.87052 85.38557 94.15539 18.72867 22.50000 17.30304 67.50000 7.16715 301.59289 9.39756 6.21252 12.64851
19.00 48.00000 47.07769 47.07769 48.00000 18.72867 57.72436 57.22040 6.14666 9.49414 6.06310 83.93690 88.16163 88.65757 94.15539 18.72867 22.50000 17.30304 67.50000 7.16715 301.59289 9.54657 5.97974 12.18170
20.00 48.00000 47.07769 47.07769 48.00000 18.72867 59.03624 58.54359 5.92621 9.63021 5.84328 84.15672 91.50259 91.98051 94.15539 18.72867 22.50000 17.30304 67.50000 7.16715 301.59289 9.67956 5.76066 11.74162
21.00 48.00000 47.07769 47.07769 48.00000 18.72867 60.25512 59.77392 5.71826 9.75211 5.63617 84.36383 94.88812 95.34908 94.15539 18.72867 22.50000 17.30304 67.50000 7.16715 301.59289 9.79857 5.55446 11.32680
22.00 48.00000 47.07769 47.07769 48.00000 18.72867 61.38954 60.91979 5.52209 9.86161 5.44099 84.55901 98.31363 98.75860 94.15539 18.72867 22.50000 17.30304 67.50000 7.16715 301.59289 9.90536 5.36035 10.93576
23.00 48.00000 47.07769 47.07769 48.00000 18.72867 62.44719 61.98878 5.33697 9.96020 5.25699 84.74301 101.77508 102.20498 94.15539 18.72867 22.50000 17.30304 67.50000 7.16715 301.59289 10.00143 5.17754 10.56700
24.00 48.00000 47.07769 47.07769 48.00000 18.72867 63.43495 62.98771 5.16222 10.04922 5.08344 84.91656 105.26892 105.68461 94.15539 18.72867 22.50000 17.30304 67.50000 7.16715 301.59289 10.08809 5.00525 10.21908
Pitch Radius apothem radius apothem multiplier apothem multiplier * apothem side wall multiplier * apothem Pitch Angle Hip Angle Hip Side Cut Angle Hip Backing Angle Jack Rafter Side Cut Angle Jack Rafter Side Cut Angle 2 Rafter Length Hip Length Span Wall Length Projection Angle A Projection A Projection Angle B Projection B Circumference Freize Block Miter Angle Freize Block Bevel Angle Surface Angle


Roof Surface Angle A Bay # 0 = 78.75000
Roof Surface Angle C Bay # 0 = 22.50000
Roof Surface Angle B Bay # 0 = 78.75000

Roof Surface Angle A Bay # 1 = 78.78787
Roof Surface Angle C Bay # 1 = 22.42425
Roof Surface Angle B Bay # 1 = 78.78787

Roof Surface Angle A Bay # 2 = 78.89924
Roof Surface Angle C Bay # 2 = 22.20152
Roof Surface Angle B Bay # 2 = 78.89924

Roof Surface Angle A Bay # 3 = 79.07770
Roof Surface Angle C Bay # 3 = 21.84460
Roof Surface Angle B Bay # 3 = 79.07770

Roof Surface Angle A Bay # 4 = 79.31367
Roof Surface Angle C Bay # 4 = 21.37266
Roof Surface Angle B Bay # 4 = 79.31367

Roof Surface Angle A Bay # 5 = 79.59573
Roof Surface Angle C Bay # 5 = 20.80854
Roof Surface Angle B Bay # 5 = 79.59573

Roof Surface Angle A Bay # 6 = 79.91191
Roof Surface Angle C Bay # 6 = 20.17618
Roof Surface Angle B Bay # 6 = 79.91191

Roof Surface Angle A Bay # 7 = 80.25084
Roof Surface Angle C Bay # 7 = 19.49832
Roof Surface Angle B Bay # 7 = 80.25084

Roof Surface Angle A Bay # 8 = 80.60244
Roof Surface Angle C Bay # 8 = 18.79511
Roof Surface Angle B Bay # 8 = 80.60244

Roof Surface Angle A Bay # 9 = 80.95834
Roof Surface Angle C Bay # 9 = 18.08332
Roof Surface Angle B Bay # 9 = 80.95834

Roof Surface Angle A Bay # 10 = 81.31191
Roof Surface Angle C Bay # 10 = 17.37617
Roof Surface Angle B Bay # 10 = 81.31191

Roof Surface Angle A Bay # 11 = 81.65822
Roof Surface Angle C Bay # 11 = 16.68357
Roof Surface Angle B Bay # 11 = 81.65822

Roof Surface Angle A Bay # 12 = 81.99374
Roof Surface Angle C Bay # 12 = 16.01252
Roof Surface Angle B Bay # 12 = 81.99374

Roof Surface Angle A Bay # 13 = 82.31615
Roof Surface Angle C Bay # 13 = 15.36770
Roof Surface Angle B Bay # 13 = 82.31615

Roof Surface Angle A Bay # 14 = 82.62405
Roof Surface Angle C Bay # 14 = 14.75189
Roof Surface Angle B Bay # 14 = 82.62405

Roof Surface Angle A Bay # 15 = 82.91676
Roof Surface Angle C Bay # 15 = 14.16648
Roof Surface Angle B Bay # 15 = 82.91676

Roof Surface Angle A Bay # 16 = 83.19409
Roof Surface Angle C Bay # 16 = 13.61182
Roof Surface Angle B Bay # 16 = 83.19409

Roof Surface Angle A Bay # 17 = 83.45624
Roof Surface Angle C Bay # 17 = 13.08753
Roof Surface Angle B Bay # 17 = 83.45624

Roof Surface Angle A Bay # 18 = 83.70364
Roof Surface Angle C Bay # 18 = 12.59272
Roof Surface Angle B Bay # 18 = 83.70364

Roof Surface Angle A Bay # 19 = 83.93690
Roof Surface Angle C Bay # 19 = 12.12620
Roof Surface Angle B Bay # 19 = 83.93690

Roof Surface Angle A Bay # 20 = 84.15672
Roof Surface Angle C Bay # 20 = 11.68656
Roof Surface Angle B Bay # 20 = 84.15672

Roof Surface Angle A Bay # 21 = 84.36383
Roof Surface Angle C Bay # 21 = 11.27233
Roof Surface Angle B Bay # 21 = 84.36383

Roof Surface Angle A Bay # 22 = 84.55901
Roof Surface Angle C Bay # 22 = 10.88197
Roof Surface Angle B Bay # 22 = 84.55901

Roof Surface Angle A Bay # 23 = 84.74301
Roof Surface Angle C Bay # 23 = 10.51398
Roof Surface Angle B Bay # 23 = 84.74301

Roof Surface Angle A Bay # 24 = 84.91656
Roof Surface Angle C Bay # 24 = 10.16688
Roof Surface Angle B Bay # 24 = 84.91656