Developmental Geometry for a Pyramid with an (12 sided) Polygonal Base
Polygonal Trigonometric Functions are to 5 Decimal Places


central angle = 30
working angle = 15
plan angle = 75
miter angle = 3.22 & 12
hip run per foot = 12.423314164921
apothem multiplier = secant(360 ( N 2 ))
side wall multiplier = tan((360 (N 2 )) 2
apothem_multiplier = 1.03527618041008
side_wall_multiplier = 0.535898384862245
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 46.36444 46.36444 48.00000 24.84663 0.00000 0.00000 15.00000 0.00000 15.00000 75.00000 46.36444 48.00000 92.72888 24.84663 30.00000 21.51781 60.00000 12.42331 301.59289 0.00000 15.00000 30.00000
1.00 48.00000 46.36444 46.36444 48.00000 24.84663 4.76364 4.60203 14.95381 1.23160 14.95051 75.04949 46.52515 48.15525 92.72888 24.84663 30.00000 21.51781 60.00000 12.42331 301.59289 1.27473 14.94698 29.90328
2.00 48.00000 46.36444 46.36444 48.00000 24.84663 9.46232 9.14544 14.81776 2.43865 14.80493 75.19507 47.00398 48.61803 92.72888 24.84663 30.00000 21.51781 60.00000 12.42331 301.59289 2.52228 14.79122 29.61864
3.00 48.00000 46.36444 46.36444 48.00000 24.84663 14.03624 13.57596 14.59904 3.59898 14.57147 75.42853 47.79137 49.37969 92.72888 24.84663 30.00000 21.51781 60.00000 12.42331 301.59289 3.71827 14.54210 29.16179
4.00 48.00000 46.36444 46.36444 48.00000 24.84663 18.43495 17.84728 14.30849 4.69467 14.26245 75.73755 48.87241 50.42669 92.72888 24.84663 30.00000 21.51781 60.00000 12.42331 301.59289 4.84327 14.21359 28.55631
5.00 48.00000 46.36444 46.36444 48.00000 24.84663 22.61986 21.92326 13.95923 5.71302 13.89259 76.10741 50.22814 51.74172 92.72888 24.84663 30.00000 21.51781 60.00000 12.42331 301.59289 5.88398 13.82221 27.83054
6.00 48.00000 46.36444 46.36444 48.00000 24.84663 26.56505 25.77882 13.56521 6.64674 13.47737 76.52263 51.83702 53.30493 92.72888 24.84663 30.00000 21.51781 60.00000 12.42331 301.59289 6.83320 13.38509 27.01439
7.00 48.00000 46.36444 46.36444 48.00000 24.84663 30.25644 29.39938 13.13995 7.49337 13.03158 76.96842 53.67628 55.09521 92.72888 24.84663 30.00000 21.51781 60.00000 12.42331 301.59289 7.68911 12.91836 26.13657
8.00 48.00000 46.36444 46.36444 48.00000 24.84663 33.69007 32.77953 12.69571 8.25430 12.56839 77.43161 55.72312 57.09120 92.72888 24.84663 30.00000 21.51781 60.00000 12.42331 301.59289 8.45406 12.43609 25.22280
9.00 48.00000 46.36444 46.36444 48.00000 24.84663 36.86990 35.92124 12.24291 8.93370 12.09879 77.90121 57.95555 59.27212 92.72888 24.84663 30.00000 21.51781 60.00000 12.42331 301.59289 9.13326 11.94984 24.29473
10.00 48.00000 46.36444 46.36444 48.00000 24.84663 39.80557 38.83192 11.79004 9.53743 11.63154 78.36846 60.35297 61.61834 92.72888 24.84663 30.00000 21.51781 60.00000 12.42331 301.59289 9.73361 11.46857 23.36966
11.00 48.00000 46.36444 46.36444 48.00000 24.84663 42.51045 41.52271 11.34363 10.07228 11.17323 78.82677 62.89653 64.11172 92.72888 24.84663 30.00000 21.51781 60.00000 12.42331 301.59289 10.26278 10.99886 22.46079
12.00 48.00000 46.36444 46.36444 48.00000 24.84663 45.00000 44.00703 10.90851 10.54529 10.72858 79.27142 65.56922 66.73576 92.72888 24.84663 30.00000 21.51781 60.00000 12.42331 301.59289 10.72858 10.54529 21.57764
13.00 48.00000 46.36444 46.36444 48.00000 24.84663 47.29061 46.29944 10.48805 10.96335 10.30077 79.69923 68.35589 69.47565 92.72888 24.84663 30.00000 21.51781 60.00000 12.42331 301.59289 11.13849 10.11077 20.72669
14.00 48.00000 46.36444 46.36444 48.00000 24.84663 49.39871 48.41480 10.08443 11.33295 9.89172 80.10828 71.24317 72.31824 92.72888 24.84663 30.00000 21.51781 60.00000 12.42331 301.59289 11.49944 9.69697 19.91199
15.00 48.00000 46.36444 46.36444 48.00000 24.84663 51.34019 50.36773 9.69891 11.66001 9.50245 80.49755 74.21932 75.25188 92.72888 24.84663 30.00000 21.51781 60.00000 12.42331 301.59289 11.81769 9.30460 19.13573
16.00 48.00000 46.36444 46.36444 48.00000 24.84663 53.13010 52.17219 9.33205 11.94984 9.13326 80.86674 77.27407 78.26634 92.72888 24.84663 30.00000 21.51781 60.00000 12.42331 301.59289 12.09879 8.93370 18.39871
17.00 48.00000 46.36444 46.36444 48.00000 24.84663 54.78241 53.84129 8.98390 12.20715 8.78397 81.21603 80.39846 81.35263 92.72888 24.84663 30.00000 21.51781 60.00000 12.42331 301.59289 12.34761 8.58385 17.70072
18.00 48.00000 46.36444 46.36444 48.00000 24.84663 56.30993 55.38718 8.65415 12.43609 8.45406 81.54594 83.58468 84.50289 92.72888 24.84663 30.00000 21.51781 60.00000 12.42331 301.59289 12.56839 8.25430 17.04084
19.00 48.00000 46.36444 46.36444 48.00000 24.84663 57.72436 56.82099 8.34223 12.64024 8.14278 81.85722 86.82593 87.71021 92.72888 24.84663 30.00000 21.51781 60.00000 12.42331 301.59289 12.76478 7.94414 16.41770
20.00 48.00000 46.36444 46.36444 48.00000 24.84663 59.03624 58.15287 8.04741 12.82274 7.84925 82.15075 90.11627 90.96857 92.72888 24.84663 30.00000 21.51781 60.00000 12.42331 301.59289 12.93995 7.65231 15.82964
21.00 48.00000 46.36444 46.36444 48.00000 24.84663 60.25512 59.39202 7.76886 12.98629 7.57250 82.42750 93.45052 94.27268 92.72888 24.84663 30.00000 21.51781 60.00000 12.42331 301.59289 13.09662 7.37773 15.27484
22.00 48.00000 46.36444 46.36444 48.00000 24.84663 61.38954 60.54675 7.50573 13.13323 7.31156 82.68844 96.82413 97.61788 92.72888 24.84663 30.00000 21.51781 60.00000 12.42331 301.59289 13.23712 7.11932 14.75140
23.00 48.00000 46.36444 46.36444 48.00000 24.84663 62.44719 61.62456 7.25710 13.26558 7.06545 82.93455 100.23313 101.00010 92.72888 24.84663 30.00000 21.51781 60.00000 12.42331 301.59289 13.36346 6.87599 14.25741
24.00 48.00000 46.36444 46.36444 48.00000 24.84663 63.43495 62.63219 7.02212 13.38509 6.83320 83.16680 103.67404 104.41573 92.72888 24.84663 30.00000 21.51781 60.00000 12.42331 301.59289 13.47737 6.64674 13.79103
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 = 75.00000
Roof Surface Angle C Bay # 0 = 30.00000
Roof Surface Angle B Bay # 0 = 75.00000

Roof Surface Angle A Bay # 1 = 75.04949
Roof Surface Angle C Bay # 1 = 29.90102
Roof Surface Angle B Bay # 1 = 75.04949

Roof Surface Angle A Bay # 2 = 75.19507
Roof Surface Angle C Bay # 2 = 29.60986
Roof Surface Angle B Bay # 2 = 75.19507

Roof Surface Angle A Bay # 3 = 75.42853
Roof Surface Angle C Bay # 3 = 29.14295
Roof Surface Angle B Bay # 3 = 75.42853

Roof Surface Angle A Bay # 4 = 75.73755
Roof Surface Angle C Bay # 4 = 28.52490
Roof Surface Angle B Bay # 4 = 75.73755

Roof Surface Angle A Bay # 5 = 76.10741
Roof Surface Angle C Bay # 5 = 27.78518
Roof Surface Angle B Bay # 5 = 76.10741

Roof Surface Angle A Bay # 6 = 76.52263
Roof Surface Angle C Bay # 6 = 26.95474
Roof Surface Angle B Bay # 6 = 76.52263

Roof Surface Angle A Bay # 7 = 76.96842
Roof Surface Angle C Bay # 7 = 26.06316
Roof Surface Angle B Bay # 7 = 76.96842

Roof Surface Angle A Bay # 8 = 77.43161
Roof Surface Angle C Bay # 8 = 25.13677
Roof Surface Angle B Bay # 8 = 77.43161

Roof Surface Angle A Bay # 9 = 77.90121
Roof Surface Angle C Bay # 9 = 24.19758
Roof Surface Angle B Bay # 9 = 77.90121

Roof Surface Angle A Bay # 10 = 78.36846
Roof Surface Angle C Bay # 10 = 23.26308
Roof Surface Angle B Bay # 10 = 78.36846

Roof Surface Angle A Bay # 11 = 78.82677
Roof Surface Angle C Bay # 11 = 22.34646
Roof Surface Angle B Bay # 11 = 78.82677

Roof Surface Angle A Bay # 12 = 79.27142
Roof Surface Angle C Bay # 12 = 21.45717
Roof Surface Angle B Bay # 12 = 79.27142

Roof Surface Angle A Bay # 13 = 79.69923
Roof Surface Angle C Bay # 13 = 20.60153
Roof Surface Angle B Bay # 13 = 79.69923

Roof Surface Angle A Bay # 14 = 80.10828
Roof Surface Angle C Bay # 14 = 19.78344
Roof Surface Angle B Bay # 14 = 80.10828

Roof Surface Angle A Bay # 15 = 80.49755
Roof Surface Angle C Bay # 15 = 19.00490
Roof Surface Angle B Bay # 15 = 80.49755

Roof Surface Angle A Bay # 16 = 80.86674
Roof Surface Angle C Bay # 16 = 18.26652
Roof Surface Angle B Bay # 16 = 80.86674

Roof Surface Angle A Bay # 17 = 81.21603
Roof Surface Angle C Bay # 17 = 17.56795
Roof Surface Angle B Bay # 17 = 81.21603

Roof Surface Angle A Bay # 18 = 81.54594
Roof Surface Angle C Bay # 18 = 16.90813
Roof Surface Angle B Bay # 18 = 81.54594

Roof Surface Angle A Bay # 19 = 81.85722
Roof Surface Angle C Bay # 19 = 16.28557
Roof Surface Angle B Bay # 19 = 81.85722

Roof Surface Angle A Bay # 20 = 82.15075
Roof Surface Angle C Bay # 20 = 15.69849
Roof Surface Angle B Bay # 20 = 82.15075

Roof Surface Angle A Bay # 21 = 82.42750
Roof Surface Angle C Bay # 21 = 15.14500
Roof Surface Angle B Bay # 21 = 82.42750

Roof Surface Angle A Bay # 22 = 82.68844
Roof Surface Angle C Bay # 22 = 14.62312
Roof Surface Angle B Bay # 22 = 82.68844

Roof Surface Angle A Bay # 23 = 82.93455
Roof Surface Angle C Bay # 23 = 14.13089
Roof Surface Angle B Bay # 23 = 82.93455

Roof Surface Angle A Bay # 24 = 83.16680
Roof Surface Angle C Bay # 24 = 13.66640
Roof Surface Angle B Bay # 24 = 83.16680