Developmental Geometry for a Pyramid with an (9 sided) Polygonal Base
Polygonal Trigonometric Functions are to 5 Decimal Places


central angle = 40
working angle = 20
plan angle = 70
miter angle = 4.37 & 12
hip run per foot = 12.7701332697109
apothem multiplier = secant(360 ( N 2 ))
side wall multiplier = tan((360 (N 2 )) 2
apothem_multiplier = 1.06417777247591
side_wall_multiplier = 0.727940468532405
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 45.10525 45.10525 48.00000 32.83393 0.00000 0.00000 20.00000 0.00000 20.00000 70.00000 45.10525 48.00000 90.21049 32.83393 40.00000 25.15225 50.00000 21.10525 301.59289 0.00000 20.00000 40.00000
1.00 48.00000 45.10525 45.10525 48.00000 32.83393 4.76364 4.47756 19.94378 1.62760 19.93637 70.06363 45.26159 48.14695 90.21049 32.83393 40.00000 25.15225 50.00000 21.10525 301.59289 1.73130 19.92798 39.87792
2.00 48.00000 45.10525 45.10525 48.00000 32.83393 9.46232 8.90110 19.77792 3.22331 19.74905 70.25095 45.72742 48.58512 90.21049 32.83393 40.00000 25.15225 50.00000 21.10525 301.59289 3.42429 19.71651 39.51828
3.00 48.00000 45.10525 45.10525 48.00000 32.83393 14.03624 13.22038 19.51047 4.75827 19.44828 70.55172 46.49342 49.30675 90.21049 32.83393 40.00000 25.15225 50.00000 21.10525 301.59289 5.04475 19.37857 38.93990
4.00 48.00000 45.10525 45.10525 48.00000 32.83393 18.43495 17.39217 19.15365 6.20904 19.04941 70.95059 47.54510 50.29964 90.21049 32.83393 40.00000 25.15225 50.00000 21.10525 301.59289 6.56571 18.93340 38.17125
5.00 48.00000 45.10525 45.10525 48.00000 32.83393 22.61986 21.38226 18.72243 7.55895 18.57093 71.42907 48.86402 51.54812 90.21049 32.83393 40.00000 25.15225 50.00000 21.10525 301.59289 7.96897 18.40374 37.24675
6.00 48.00000 45.10525 45.10525 48.00000 32.83393 26.56505 25.16631 18.23298 8.79827 18.03239 71.96761 50.42920 53.03415 90.21049 32.83393 40.00000 25.15225 50.00000 21.10525 301.59289 9.24509 17.81305 36.20309
7.00 48.00000 45.10525 45.10525 48.00000 32.83393 30.25644 28.72953 17.70126 9.92355 17.45262 72.54738 52.21851 54.73837 90.21049 32.83393 40.00000 25.15225 50.00000 21.10525 301.59289 10.39222 17.18331 35.07594
8.00 48.00000 45.10525 45.10525 48.00000 32.83393 33.69007 32.06557 17.14203 10.93636 16.84849 73.15151 54.20976 56.64110 90.21049 32.83393 40.00000 25.15225 50.00000 21.10525 301.59289 11.41426 16.53362 33.89764
9.00 48.00000 45.10525 45.10525 48.00000 32.83393 36.86990 35.17501 16.56816 11.84191 16.23430 73.76570 56.38156 58.72305 90.21049 32.83393 40.00000 25.15225 50.00000 21.10525 301.59289 12.31897 15.87956 32.69585
10.00 48.00000 45.10525 45.10525 48.00000 32.83393 39.80557 38.06369 15.99035 12.64772 15.62151 74.37849 58.71387 60.96586 90.21049 32.83393 40.00000 25.15225 50.00000 21.10525 301.59289 13.11635 15.23313 31.49304
11.00 48.00000 45.10525 45.10525 48.00000 32.83393 42.51045 40.74111 15.41715 13.36252 15.01887 74.98113 61.18835 63.35244 90.21049 32.83393 40.00000 25.15225 50.00000 21.10525 301.59289 13.81730 14.60309 30.30665
12.00 48.00000 45.10525 45.10525 48.00000 32.83393 45.00000 43.21918 14.85505 13.99545 14.43276 75.56724 63.78845 65.86716 90.21049 32.83393 40.00000 25.15225 50.00000 21.10525 301.59289 14.43276 13.99545 29.14958
13.00 48.00000 45.10525 45.10525 48.00000 32.83393 47.29061 45.51106 14.30878 14.55549 13.86754 76.13246 66.49944 68.49593 90.21049 32.83393 40.00000 25.15225 50.00000 21.10525 301.59289 14.97313 13.41399 28.03086
14.00 48.00000 45.10525 45.10525 48.00000 32.83393 49.39871 47.63042 13.78161 15.05114 13.32597 76.67403 69.30830 71.22610 90.21049 32.83393 40.00000 25.15225 50.00000 21.10525 301.59289 15.44797 12.86084 26.95641
15.00 48.00000 45.10525 45.10525 48.00000 32.83393 51.34019 49.59085 13.27561 15.49016 12.80959 77.19041 72.20362 74.04647 90.21049 32.83393 40.00000 25.15225 50.00000 21.10525 301.59289 15.86584 12.33682 25.92966
16.00 48.00000 45.10525 45.10525 48.00000 32.83393 53.13010 51.40547 12.79194 15.87956 12.31897 77.68103 75.17541 76.94712 90.21049 32.83393 40.00000 25.15225 50.00000 21.10525 301.59289 16.23430 11.84191 24.95220
17.00 48.00000 45.10525 45.10525 48.00000 32.83393 54.78241 53.08670 12.33103 16.22556 11.85405 78.14595 78.21495 79.91930 90.21049 32.83393 40.00000 25.15225 50.00000 21.10525 301.59289 16.55995 11.37545 24.02423
18.00 48.00000 45.10525 45.10525 48.00000 32.83393 56.30993 54.64613 11.89282 16.53362 11.41426 78.58574 81.31464 82.95533 90.21049 32.83393 40.00000 25.15225 50.00000 21.10525 301.59289 16.84849 10.93636 23.14499
19.00 48.00000 45.10525 45.10525 48.00000 32.83393 57.72436 56.09447 11.47686 16.80853 10.99874 79.00126 84.46786 86.04845 90.21049 32.83393 40.00000 25.15225 50.00000 21.10525 301.59289 17.10485 10.52336 22.31301
20.00 48.00000 45.10525 45.10525 48.00000 32.83393 59.03624 57.44150 11.08247 17.05442 10.60643 79.39357 87.66884 89.19273 90.21049 32.83393 40.00000 25.15225 50.00000 21.10525 301.59289 17.33324 10.13499 21.52642
21.00 48.00000 45.10525 45.10525 48.00000 32.83393 60.25512 58.69615 10.70876 17.27490 10.23615 79.76385 90.91253 92.38292 90.21049 32.83393 40.00000 25.15225 50.00000 21.10525 301.59289 17.53730 9.76977 20.78306
22.00 48.00000 45.10525 45.10525 48.00000 32.83393 61.38954 59.86652 10.35480 17.47310 9.88665 80.11335 94.19452 95.61446 90.21049 32.83393 40.00000 25.15225 50.00000 21.10525 301.59289 17.72013 9.42620 20.08065
23.00 48.00000 45.10525 45.10525 48.00000 32.83393 62.44719 60.95995 10.01955 17.65170 9.55671 80.44329 97.51094 98.88326 90.21049 32.83393 40.00000 25.15225 50.00000 21.10525 301.59289 17.88440 9.10283 19.41683
24.00 48.00000 45.10525 45.10525 48.00000 32.83393 63.43495 61.98305 9.70198 17.81305 9.24509 80.75491 100.85840 102.18578 90.21049 32.83393 40.00000 25.15225 50.00000 21.10525 301.59289 18.03239 8.79827 18.78931
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 = 70.00000
Roof Surface Angle C Bay # 0 = 40.00000
Roof Surface Angle B Bay # 0 = 70.00000

Roof Surface Angle A Bay # 1 = 70.06363
Roof Surface Angle C Bay # 1 = 39.87273
Roof Surface Angle B Bay # 1 = 70.06363

Roof Surface Angle A Bay # 2 = 70.25095
Roof Surface Angle C Bay # 2 = 39.49811
Roof Surface Angle B Bay # 2 = 70.25095

Roof Surface Angle A Bay # 3 = 70.55172
Roof Surface Angle C Bay # 3 = 38.89656
Roof Surface Angle B Bay # 3 = 70.55172

Roof Surface Angle A Bay # 4 = 70.95059
Roof Surface Angle C Bay # 4 = 38.09882
Roof Surface Angle B Bay # 4 = 70.95059

Roof Surface Angle A Bay # 5 = 71.42907
Roof Surface Angle C Bay # 5 = 37.14187
Roof Surface Angle B Bay # 5 = 71.42907

Roof Surface Angle A Bay # 6 = 71.96761
Roof Surface Angle C Bay # 6 = 36.06479
Roof Surface Angle B Bay # 6 = 71.96761

Roof Surface Angle A Bay # 7 = 72.54738
Roof Surface Angle C Bay # 7 = 34.90523
Roof Surface Angle B Bay # 7 = 72.54738

Roof Surface Angle A Bay # 8 = 73.15151
Roof Surface Angle C Bay # 8 = 33.69699
Roof Surface Angle B Bay # 8 = 73.15151

Roof Surface Angle A Bay # 9 = 73.76570
Roof Surface Angle C Bay # 9 = 32.46860
Roof Surface Angle B Bay # 9 = 73.76570

Roof Surface Angle A Bay # 10 = 74.37849
Roof Surface Angle C Bay # 10 = 31.24301
Roof Surface Angle B Bay # 10 = 74.37849

Roof Surface Angle A Bay # 11 = 74.98113
Roof Surface Angle C Bay # 11 = 30.03773
Roof Surface Angle B Bay # 11 = 74.98113

Roof Surface Angle A Bay # 12 = 75.56724
Roof Surface Angle C Bay # 12 = 28.86551
Roof Surface Angle B Bay # 12 = 75.56724

Roof Surface Angle A Bay # 13 = 76.13246
Roof Surface Angle C Bay # 13 = 27.73507
Roof Surface Angle B Bay # 13 = 76.13246

Roof Surface Angle A Bay # 14 = 76.67403
Roof Surface Angle C Bay # 14 = 26.65195
Roof Surface Angle B Bay # 14 = 76.67403

Roof Surface Angle A Bay # 15 = 77.19041
Roof Surface Angle C Bay # 15 = 25.61917
Roof Surface Angle B Bay # 15 = 77.19041

Roof Surface Angle A Bay # 16 = 77.68103
Roof Surface Angle C Bay # 16 = 24.63794
Roof Surface Angle B Bay # 16 = 77.68103

Roof Surface Angle A Bay # 17 = 78.14595
Roof Surface Angle C Bay # 17 = 23.70809
Roof Surface Angle B Bay # 17 = 78.14595

Roof Surface Angle A Bay # 18 = 78.58574
Roof Surface Angle C Bay # 18 = 22.82852
Roof Surface Angle B Bay # 18 = 78.58574

Roof Surface Angle A Bay # 19 = 79.00126
Roof Surface Angle C Bay # 19 = 21.99749
Roof Surface Angle B Bay # 19 = 79.00126

Roof Surface Angle A Bay # 20 = 79.39357
Roof Surface Angle C Bay # 20 = 21.21287
Roof Surface Angle B Bay # 20 = 79.39357

Roof Surface Angle A Bay # 21 = 79.76385
Roof Surface Angle C Bay # 21 = 20.47230
Roof Surface Angle B Bay # 21 = 79.76385

Roof Surface Angle A Bay # 22 = 80.11335
Roof Surface Angle C Bay # 22 = 19.77331
Roof Surface Angle B Bay # 22 = 80.11335

Roof Surface Angle A Bay # 23 = 80.44329
Roof Surface Angle C Bay # 23 = 19.11342
Roof Surface Angle B Bay # 23 = 80.44329

Roof Surface Angle A Bay # 24 = 80.75491
Roof Surface Angle C Bay # 24 = 18.49019
Roof Surface Angle B Bay # 24 = 80.75491