Developmental Geometry for a Pyramid with an (11 sided) Polygonal Base
Polygonal Trigonometric Functions are to 5 Decimal Places


central angle = 32.7272727272727
working angle = 16.3636363636364
plan angle = 73.6363636363636
miter angle = 3.52 & 12
hip run per foot = 12.5066053947169
apothem multiplier = secant(360 ( N 2 ))
side wall multiplier = tan((360 (N 2 )) 2
apothem_multiplier = 1.04221711622641
side_wall_multiplier = 0.587252985876733
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 46.05566 46.05566 48.00000 27.04633 0.00000 0.00000 16.36364 0.00000 16.36364 73.63636 46.05566 48.00000 92.11133 27.04633 32.72727 22.75282 57.27273 14.62235 301.59289 0.00000 16.36364 32.72727
1.00 48.00000 46.05566 46.05566 48.00000 27.04633 4.76364 4.57152 16.31435 1.34065 16.31012 73.68988 46.21530 48.15319 92.11133 27.04633 32.72727 22.75282 57.27273 14.62235 301.59289 1.39684 16.30553 32.62316
2.00 48.00000 46.05566 46.05566 48.00000 27.04633 9.46232 9.08556 16.16912 2.65469 16.15268 73.84732 46.69094 48.60988 92.11133 27.04633 32.72727 22.75282 57.27273 14.62235 301.59289 2.76363 16.13487 32.31666
3.00 48.00000 46.05566 46.05566 48.00000 27.04633 14.03624 13.48887 15.93547 3.91808 15.90011 74.09989 47.47309 49.36163 92.11133 27.04633 32.72727 22.75282 57.27273 14.62235 301.59289 4.07344 15.86197 31.82450
4.00 48.00000 46.05566 46.05566 48.00000 27.04633 18.43495 17.73589 15.62475 5.11135 15.56563 74.43437 48.54693 50.39524 92.11133 27.04633 32.72727 22.75282 57.27273 14.62235 301.59289 5.30487 15.50218 31.17177
5.00 48.00000 46.05566 46.05566 48.00000 27.04633 22.61986 21.79097 15.25074 6.22071 15.16509 74.83491 49.89363 51.69382 92.11133 27.04633 32.72727 22.75282 57.27273 14.62235 301.59289 6.44330 15.07367 30.38872
6.00 48.00000 46.05566 46.05566 48.00000 27.04633 26.56505 25.62920 14.82816 7.23820 14.71514 75.28486 51.49180 53.23797 92.11133 27.04633 32.72727 22.75282 57.27273 14.62235 301.59289 7.48092 14.59526 29.50731
7.00 48.00000 46.05566 46.05566 48.00000 27.04633 30.25644 29.23592 14.37134 8.16110 14.23174 75.76826 53.31881 55.00701 92.11133 27.04633 32.72727 22.75282 57.27273 14.62235 301.59289 8.41585 14.08462 28.55834
8.00 48.00000 46.05566 46.05566 48.00000 27.04633 33.69007 32.60550 13.89331 8.99087 13.72911 76.27089 55.35202 56.98001 92.11133 27.04633 32.72727 22.75282 57.27273 14.62235 301.59289 9.25080 13.55718 27.56948
9.00 48.00000 46.05566 46.05566 48.00000 27.04633 36.86990 35.73954 13.40528 9.73198 13.21919 76.78081 57.56958 59.13656 92.11133 27.04633 32.72727 22.75282 57.27273 14.62235 301.59289 9.99160 13.02558 26.56409
10.00 48.00000 46.05566 46.05566 48.00000 27.04633 39.80557 38.64504 12.91636 10.39078 12.71147 77.28853 59.95104 61.45733 92.11133 27.04633 32.72727 22.75282 57.27273 14.62235 301.59289 10.64595 12.49961 25.56097
11.00 48.00000 46.05566 46.05566 48.00000 27.04633 42.51045 41.33277 12.43366 10.97459 12.21315 77.78685 62.47766 63.92444 92.11133 27.04633 32.72727 22.75282 57.27273 14.62235 301.59289 11.22235 11.98645 24.57447
12.00 48.00000 46.05566 46.05566 48.00000 27.04633 45.00000 43.81574 11.96247 11.49106 11.72940 78.27060 65.13254 66.52161 92.11133 27.04633 32.72727 22.75282 57.27273 14.62235 301.59289 11.72940 11.49106 23.61502
13.00 48.00000 46.05566 46.05566 48.00000 27.04633 47.29061 46.10818 11.50653 11.94766 11.26370 78.73630 67.90065 69.23420 92.11133 27.04633 32.72727 22.75282 57.27273 14.62235 301.59289 12.17537 11.01661 22.68978
14.00 48.00000 46.05566 46.05566 48.00000 27.04633 49.39871 48.22466 11.06828 12.35143 10.81821 79.18179 70.76871 72.04919 92.11133 27.04633 32.72727 22.75282 57.27273 14.62235 301.59289 12.56787 10.56490 21.80329
15.00 48.00000 46.05566 46.05566 48.00000 27.04633 51.34019 50.17954 10.64919 12.70881 10.39405 79.60595 73.72503 74.95503 92.11133 27.04633 32.72727 22.75282 57.27273 14.62235 301.59289 12.91378 10.13668 20.95802
16.00 48.00000 46.05566 46.05566 48.00000 27.04633 53.13010 51.98658 10.24996 13.02558 9.99160 80.00840 76.75944 77.94156 92.11133 27.04633 32.72727 22.75282 57.27273 14.62235 301.59289 13.21919 9.73198 20.15496
17.00 48.00000 46.05566 46.05566 48.00000 27.04633 54.78241 53.65873 9.87071 13.30687 9.61070 80.38930 79.86302 80.99987 92.11133 27.04633 32.72727 22.75282 57.27273 14.62235 301.59289 13.48942 9.35032 19.39397
18.00 48.00000 46.05566 46.05566 48.00000 27.04633 56.30993 55.20799 9.51117 13.55718 9.25080 80.74920 83.02803 84.12211 92.11133 27.04633 32.72727 22.75282 57.27273 14.62235 301.59289 13.72911 8.99087 18.67415
19.00 48.00000 46.05566 46.05566 48.00000 27.04633 57.72436 56.64539 9.17079 13.78043 8.91111 81.08889 86.24769 87.30143 92.11133 27.04633 32.72727 22.75282 57.27273 14.62235 301.59289 13.94226 8.65261 17.99408
20.00 48.00000 46.05566 46.05566 48.00000 27.04633 59.03624 57.98101 8.84882 13.98003 8.59069 81.40931 89.51612 90.53182 92.11133 27.04633 32.72727 22.75282 57.27273 14.62235 301.59289 14.13233 8.33440 17.35201
21.00 48.00000 46.05566 46.05566 48.00000 27.04633 60.25512 59.22398 8.54443 14.15893 8.28852 81.71148 92.82816 93.80801 92.11133 27.04633 32.72727 22.75282 57.27273 14.62235 301.59289 14.30228 8.03503 16.74600
22.00 48.00000 46.05566 46.05566 48.00000 27.04633 61.38954 60.38255 8.25668 14.31968 8.00353 81.99647 96.17930 97.12535 92.11133 27.04633 32.72727 22.75282 57.27273 14.62235 301.59289 14.45465 7.75331 16.17404
23.00 48.00000 46.05566 46.05566 48.00000 27.04633 62.44719 61.46418 7.98466 14.46448 7.73468 82.26532 99.56560 100.47977 92.11133 27.04633 32.72727 22.75282 57.27273 14.62235 301.59289 14.59165 7.48808 15.63408
24.00 48.00000 46.05566 46.05566 48.00000 27.04633 63.43495 62.47559 7.72741 14.59526 7.48092 82.51908 102.98359 103.86769 92.11133 27.04633 32.72727 22.75282 57.27273 14.62235 301.59289 14.71514 7.23820 15.12414
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 = 73.63636
Roof Surface Angle C Bay # 0 = 32.72727
Roof Surface Angle B Bay # 0 = 73.63636

Roof Surface Angle A Bay # 1 = 73.68988
Roof Surface Angle C Bay # 1 = 32.62024
Roof Surface Angle B Bay # 1 = 73.68988

Roof Surface Angle A Bay # 2 = 73.84732
Roof Surface Angle C Bay # 2 = 32.30535
Roof Surface Angle B Bay # 2 = 73.84732

Roof Surface Angle A Bay # 3 = 74.09989
Roof Surface Angle C Bay # 3 = 31.80022
Roof Surface Angle B Bay # 3 = 74.09989

Roof Surface Angle A Bay # 4 = 74.43437
Roof Surface Angle C Bay # 4 = 31.13127
Roof Surface Angle B Bay # 4 = 74.43437

Roof Surface Angle A Bay # 5 = 74.83491
Roof Surface Angle C Bay # 5 = 30.33018
Roof Surface Angle B Bay # 5 = 74.83491

Roof Surface Angle A Bay # 6 = 75.28486
Roof Surface Angle C Bay # 6 = 29.43028
Roof Surface Angle B Bay # 6 = 75.28486

Roof Surface Angle A Bay # 7 = 75.76826
Roof Surface Angle C Bay # 7 = 28.46347
Roof Surface Angle B Bay # 7 = 75.76826

Roof Surface Angle A Bay # 8 = 76.27089
Roof Surface Angle C Bay # 8 = 27.45822
Roof Surface Angle B Bay # 8 = 76.27089

Roof Surface Angle A Bay # 9 = 76.78081
Roof Surface Angle C Bay # 9 = 26.43837
Roof Surface Angle B Bay # 9 = 76.78081

Roof Surface Angle A Bay # 10 = 77.28853
Roof Surface Angle C Bay # 10 = 25.42294
Roof Surface Angle B Bay # 10 = 77.28853

Roof Surface Angle A Bay # 11 = 77.78685
Roof Surface Angle C Bay # 11 = 24.42631
Roof Surface Angle B Bay # 11 = 77.78685

Roof Surface Angle A Bay # 12 = 78.27060
Roof Surface Angle C Bay # 12 = 23.45881
Roof Surface Angle B Bay # 12 = 78.27060

Roof Surface Angle A Bay # 13 = 78.73630
Roof Surface Angle C Bay # 13 = 22.52741
Roof Surface Angle B Bay # 13 = 78.73630

Roof Surface Angle A Bay # 14 = 79.18179
Roof Surface Angle C Bay # 14 = 21.63642
Roof Surface Angle B Bay # 14 = 79.18179

Roof Surface Angle A Bay # 15 = 79.60595
Roof Surface Angle C Bay # 15 = 20.78810
Roof Surface Angle B Bay # 15 = 79.60595

Roof Surface Angle A Bay # 16 = 80.00840
Roof Surface Angle C Bay # 16 = 19.98321
Roof Surface Angle B Bay # 16 = 80.00840

Roof Surface Angle A Bay # 17 = 80.38930
Roof Surface Angle C Bay # 17 = 19.22140
Roof Surface Angle B Bay # 17 = 80.38930

Roof Surface Angle A Bay # 18 = 80.74920
Roof Surface Angle C Bay # 18 = 18.50160
Roof Surface Angle B Bay # 18 = 80.74920

Roof Surface Angle A Bay # 19 = 81.08889
Roof Surface Angle C Bay # 19 = 17.82222
Roof Surface Angle B Bay # 19 = 81.08889

Roof Surface Angle A Bay # 20 = 81.40931
Roof Surface Angle C Bay # 20 = 17.18138
Roof Surface Angle B Bay # 20 = 81.40931

Roof Surface Angle A Bay # 21 = 81.71148
Roof Surface Angle C Bay # 21 = 16.57703
Roof Surface Angle B Bay # 21 = 81.71148

Roof Surface Angle A Bay # 22 = 81.99647
Roof Surface Angle C Bay # 22 = 16.00706
Roof Surface Angle B Bay # 22 = 81.99647

Roof Surface Angle A Bay # 23 = 82.26532
Roof Surface Angle C Bay # 23 = 15.46935
Roof Surface Angle B Bay # 23 = 82.26532

Roof Surface Angle A Bay # 24 = 82.51908
Roof Surface Angle C Bay # 24 = 14.96184
Roof Surface Angle B Bay # 24 = 82.51908