Developmental Geometry for a Pyramid with an (10 sided) Polygonal Base
Polygonal Trigonometric Functions are to 5 Decimal Places


central angle = 36
working angle = 18
plan angle = 72
miter angle = 3.90 & 12
hip run per foot = 12.6175466908592
apothem multiplier = secant(360 ( N 2 ))
side wall multiplier = tan((360 (N 2 )) 2
apothem_multiplier = 1.05146222423827
side_wall_multiplier = 0.649839392465813
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 45.65071 45.65071 48.00000 29.66563 0.00000 0.00000 18.00000 0.00000 18.00000 72.00000 45.65071 48.00000 91.30143 29.66563 36.00000 24.00000 54.00000 17.43702 301.59289 0.00000 18.00000 36.00000
1.00 48.00000 45.65071 45.65071 48.00000 29.66563 4.76364 4.53149 17.94735 1.47051 17.94182 72.05818 45.80895 48.15052 91.30143 29.66563 36.00000 24.00000 54.00000 17.43702 301.59289 1.54564 17.93571 35.88747
2.00 48.00000 45.65071 45.65071 48.00000 29.66563 9.46232 9.00699 17.79212 2.91200 17.77059 72.22941 46.28041 48.59926 91.30143 29.66563 36.00000 24.00000 54.00000 17.43702 301.59289 3.05763 17.74688 35.55609
3.00 48.00000 45.65071 45.65071 48.00000 29.66563 14.03624 13.37454 17.54213 4.29821 17.49581 72.50419 47.05568 49.33811 91.30143 29.66563 36.00000 24.00000 54.00000 17.43702 301.59289 4.50586 17.44502 35.02363
4.00 48.00000 45.65071 45.65071 48.00000 29.66563 18.43495 17.58960 17.20923 5.60788 17.13170 72.86830 48.12008 50.35429 91.30143 29.66563 36.00000 24.00000 54.00000 17.43702 301.59289 5.86648 17.04719 34.31684
5.00 48.00000 45.65071 45.65071 48.00000 29.66563 22.61986 21.61711 16.80783 6.82589 16.69535 73.30465 49.45494 51.63142 91.30143 29.66563 36.00000 24.00000 54.00000 17.43702 301.59289 7.12327 16.57358 33.46799
6.00 48.00000 45.65071 45.65071 48.00000 29.66563 26.56505 25.43241 16.35341 7.94350 16.20476 73.79524 51.03905 53.15070 91.30143 29.66563 36.00000 24.00000 54.00000 17.43702 301.59289 8.26770 16.04506 32.51133
7.00 48.00000 45.65071 45.65071 48.00000 29.66563 30.25644 29.02077 15.86112 8.95767 15.67724 74.32276 52.85000 54.89203 91.30143 29.66563 36.00000 24.00000 54.00000 17.43702 301.59289 9.29784 15.48121 31.47998
8.00 48.00000 45.65071 45.65071 48.00000 29.66563 33.69007 32.37624 15.34487 9.86991 15.12824 74.87176 54.86533 56.83500 91.30143 29.66563 36.00000 24.00000 54.00000 17.43702 301.59289 10.21691 14.89910 30.40380
9.00 48.00000 45.65071 45.65071 48.00000 29.66563 36.86990 35.49997 14.81665 10.68505 14.57077 75.42923 57.06339 58.95967 91.30143 29.66563 36.00000 24.00000 54.00000 17.43702 301.59289 11.03155 14.31269 29.30817
10.00 48.00000 45.65071 45.65071 48.00000 29.66563 39.80557 38.39848 14.28633 11.40997 14.01522 75.98478 59.42391 61.24715 91.30143 29.66563 36.00000 24.00000 54.00000 17.43702 301.59289 11.75045 13.73275 28.21356
11.00 48.00000 45.65071 45.65071 48.00000 29.66563 42.51045 41.08198 13.76169 12.05265 13.46950 76.53050 61.92831 63.67989 91.30143 29.66563 36.00000 24.00000 54.00000 17.43702 301.59289 12.38316 13.16718 27.13573
12.00 48.00000 45.65071 45.65071 48.00000 29.66563 45.00000 43.56300 13.24857 12.62142 12.93932 77.06068 64.55986 66.24189 91.30143 29.66563 36.00000 24.00000 54.00000 17.43702 301.59289 12.93932 12.62142 26.08621
13.00 48.00000 45.65071 45.65071 48.00000 29.66563 47.29061 45.85533 12.75113 13.12444 12.42854 77.57146 67.30363 68.91873 91.30143 29.66563 36.00000 24.00000 54.00000 17.43702 301.59289 13.42811 12.09892 25.07301
14.00 48.00000 45.65071 45.65071 48.00000 29.66563 49.39871 47.97314 12.27219 13.56941 11.93960 78.06040 70.14646 71.69755 91.30143 29.66563 36.00000 24.00000 54.00000 17.43702 301.59289 13.85801 11.60162 24.10124
15.00 48.00000 45.65071 45.65071 48.00000 29.66563 51.34019 49.93047 11.81347 13.96338 11.47378 78.52622 73.07680 74.56695 91.30143 29.66563 36.00000 24.00000 54.00000 17.43702 301.59289 14.23665 11.13033 23.17380
16.00 48.00000 45.65071 45.65071 48.00000 29.66563 53.13010 51.74081 11.37585 14.31269 11.03155 78.96845 76.08452 77.51688 91.30143 29.66563 36.00000 24.00000 54.00000 17.43702 301.59289 14.57077 10.68505 22.29192
17.00 48.00000 45.65071 45.65071 48.00000 29.66563 54.78241 53.41688 10.95958 14.62295 10.61278 79.38722 79.16082 80.53848 91.30143 29.66563 36.00000 24.00000 54.00000 17.43702 301.59289 14.86626 10.26522 21.45558
18.00 48.00000 45.65071 45.65071 48.00000 29.66563 56.30993 54.97051 10.56447 14.89910 10.21691 79.78309 82.29799 83.62399 91.30143 29.66563 36.00000 24.00000 54.00000 17.43702 301.59289 15.12824 9.86991 20.66393
19.00 48.00000 45.65071 45.65071 48.00000 29.66563 57.72436 56.41260 10.19000 15.14546 9.84310 80.15690 85.48935 86.76659 91.30143 29.66563 36.00000 24.00000 54.00000 17.43702 301.59289 15.36112 9.49798 19.91550
20.00 48.00000 45.65071 45.65071 48.00000 29.66563 59.03624 57.75310 9.83544 15.36576 9.49037 80.50963 88.72904 89.96029 91.30143 29.66563 36.00000 24.00000 54.00000 17.43702 301.59289 15.56871 9.14816 19.20847
21.00 48.00000 45.65071 45.65071 48.00000 29.66563 60.25512 59.00106 9.49990 15.56324 9.15760 80.84240 92.01195 93.19985 91.30143 29.66563 36.00000 24.00000 54.00000 17.43702 301.59289 15.75425 8.81911 18.54080
22.00 48.00000 45.65071 45.65071 48.00000 29.66563 61.38954 60.16466 9.18246 15.74073 8.84366 81.15634 95.33363 96.48064 91.30143 29.66563 36.00000 24.00000 54.00000 17.43702 301.59289 15.92056 8.50950 17.91033
23.00 48.00000 45.65071 45.65071 48.00000 29.66563 62.44719 61.25131 8.88212 15.90063 8.54740 81.45260 98.69016 99.79860 91.30143 29.66563 36.00000 24.00000 54.00000 17.43702 301.59289 16.07004 8.21805 17.31487
24.00 48.00000 45.65071 45.65071 48.00000 29.66563 63.43495 62.26770 8.59791 16.04506 8.26770 81.73230 102.07810 103.15013 91.30143 29.66563 36.00000 24.00000 54.00000 17.43702 301.59289 16.20476 7.94350 16.75228
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 = 72.00000
Roof Surface Angle C Bay # 0 = 36.00000
Roof Surface Angle B Bay # 0 = 72.00000

Roof Surface Angle A Bay # 1 = 72.05818
Roof Surface Angle C Bay # 1 = 35.88363
Roof Surface Angle B Bay # 1 = 72.05818

Roof Surface Angle A Bay # 2 = 72.22941
Roof Surface Angle C Bay # 2 = 35.54119
Roof Surface Angle B Bay # 2 = 72.22941

Roof Surface Angle A Bay # 3 = 72.50419
Roof Surface Angle C Bay # 3 = 34.99162
Roof Surface Angle B Bay # 3 = 72.50419

Roof Surface Angle A Bay # 4 = 72.86830
Roof Surface Angle C Bay # 4 = 34.26340
Roof Surface Angle B Bay # 4 = 72.86830

Roof Surface Angle A Bay # 5 = 73.30465
Roof Surface Angle C Bay # 5 = 33.39070
Roof Surface Angle B Bay # 5 = 73.30465

Roof Surface Angle A Bay # 6 = 73.79524
Roof Surface Angle C Bay # 6 = 32.40953
Roof Surface Angle B Bay # 6 = 73.79524

Roof Surface Angle A Bay # 7 = 74.32276
Roof Surface Angle C Bay # 7 = 31.35448
Roof Surface Angle B Bay # 7 = 74.32276

Roof Surface Angle A Bay # 8 = 74.87176
Roof Surface Angle C Bay # 8 = 30.25648
Roof Surface Angle B Bay # 8 = 74.87176

Roof Surface Angle A Bay # 9 = 75.42923
Roof Surface Angle C Bay # 9 = 29.14154
Roof Surface Angle B Bay # 9 = 75.42923

Roof Surface Angle A Bay # 10 = 75.98478
Roof Surface Angle C Bay # 10 = 28.03045
Roof Surface Angle B Bay # 10 = 75.98478

Roof Surface Angle A Bay # 11 = 76.53050
Roof Surface Angle C Bay # 11 = 26.93901
Roof Surface Angle B Bay # 11 = 76.53050

Roof Surface Angle A Bay # 12 = 77.06068
Roof Surface Angle C Bay # 12 = 25.87864
Roof Surface Angle B Bay # 12 = 77.06068

Roof Surface Angle A Bay # 13 = 77.57146
Roof Surface Angle C Bay # 13 = 24.85709
Roof Surface Angle B Bay # 13 = 77.57146

Roof Surface Angle A Bay # 14 = 78.06040
Roof Surface Angle C Bay # 14 = 23.87919
Roof Surface Angle B Bay # 14 = 78.06040

Roof Surface Angle A Bay # 15 = 78.52622
Roof Surface Angle C Bay # 15 = 22.94755
Roof Surface Angle B Bay # 15 = 78.52622

Roof Surface Angle A Bay # 16 = 78.96845
Roof Surface Angle C Bay # 16 = 22.06310
Roof Surface Angle B Bay # 16 = 78.96845

Roof Surface Angle A Bay # 17 = 79.38722
Roof Surface Angle C Bay # 17 = 21.22555
Roof Surface Angle B Bay # 17 = 79.38722

Roof Surface Angle A Bay # 18 = 79.78309
Roof Surface Angle C Bay # 18 = 20.43381
Roof Surface Angle B Bay # 18 = 79.78309

Roof Surface Angle A Bay # 19 = 80.15690
Roof Surface Angle C Bay # 19 = 19.68621
Roof Surface Angle B Bay # 19 = 80.15690

Roof Surface Angle A Bay # 20 = 80.50963
Roof Surface Angle C Bay # 20 = 18.98074
Roof Surface Angle B Bay # 20 = 80.50963

Roof Surface Angle A Bay # 21 = 80.84240
Roof Surface Angle C Bay # 21 = 18.31520
Roof Surface Angle B Bay # 21 = 80.84240

Roof Surface Angle A Bay # 22 = 81.15634
Roof Surface Angle C Bay # 22 = 17.68731
Roof Surface Angle B Bay # 22 = 81.15634

Roof Surface Angle A Bay # 23 = 81.45260
Roof Surface Angle C Bay # 23 = 17.09479
Roof Surface Angle B Bay # 23 = 81.45260

Roof Surface Angle A Bay # 24 = 81.73230
Roof Surface Angle C Bay # 24 = 16.53540
Roof Surface Angle B Bay # 24 = 81.73230