Developmental Geometry for a Pyramid with an (8 sided) Polygonal Base
Polygonal Trigonometric Functions are to 5 Decimal Places


central angle = 45
working angle = 22.5
plan angle = 67.5
miter angle = 4.97 & 12
hip run per foot = 12.9887064035087
apothem multiplier = secant(360 ( N 2 ))
side wall multiplier = tan((360 (N 2 )) 2
apothem_multiplier = 1.08239220029239
side_wall_multiplier = 0.82842712474619
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 44.34622 44.34622 48.00000 36.73761 0.00000 0.00000 22.50000 0.00000 22.50000 67.50000 44.34622 48.00000 88.69244 36.73761 45.00000 25.97741 45.00000 25.97741 301.59289 0.00000 22.50000 45.00000
1.00 48.00000 44.34622 44.34622 48.00000 36.73761 4.76364 4.40251 22.44020 1.82117 22.42999 67.57001 44.49993 48.14205 88.69244 36.73761 45.00000 25.97741 45.00000 25.97741 301.59289 1.97012 22.41805 44.86722
2.00 48.00000 44.34622 44.34622 48.00000 36.73761 9.46232 8.75365 22.26364 3.60702 22.22383 67.77617 44.95792 48.56570 88.69244 36.73761 45.00000 25.97741 45.00000 25.97741 301.59289 3.89562 22.17747 44.47583
3.00 48.00000 44.34622 44.34622 48.00000 36.73761 14.03624 13.00553 21.97843 5.32554 21.89254 68.10746 45.71103 49.26370 88.69244 36.73761 45.00000 25.97741 45.00000 25.97741 301.59289 5.73677 21.79319 43.84568
4.00 48.00000 44.34622 44.34622 48.00000 36.73761 18.43495 17.11673 21.59697 6.95069 21.45272 68.54728 46.74502 50.22459 88.69244 36.73761 45.00000 25.97741 45.00000 25.97741 301.59289 7.46245 21.28734 43.00682
5.00 48.00000 44.34622 44.34622 48.00000 36.73761 22.61986 21.05420 21.13456 8.46388 20.92440 69.07560 48.04174 51.43366 88.69244 36.73761 45.00000 25.97741 45.00000 25.97741 301.59289 9.05189 20.68600 41.99584
6.00 48.00000 44.34622 44.34622 48.00000 36.73761 26.56505 24.79409 20.60785 9.85418 20.32886 69.67114 49.58058 52.87388 88.69244 36.73761 45.00000 25.97741 45.00000 25.97741 301.59289 10.49462 20.01600 40.85193
7.00 48.00000 44.34622 44.34622 48.00000 36.73761 30.25644 28.32155 20.03346 11.11758 19.68665 70.31335 51.33978 54.52693 88.69244 36.73761 45.00000 25.97741 45.00000 25.97741 301.59289 11.78898 19.30240 39.61345
8.00 48.00000 44.34622 44.34622 48.00000 36.73761 33.69007 31.62973 19.42694 12.25568 19.01633 70.98367 53.29752 56.37410 88.69244 36.73761 45.00000 25.97741 45.00000 25.97741 301.59289 12.93994 18.56691 38.31547
9.00 48.00000 44.34622 44.34622 48.00000 36.73761 36.86990 34.71846 18.80203 13.27412 18.33369 71.66631 55.43277 58.39696 88.69244 36.73761 45.00000 25.97741 45.00000 25.97741 301.59289 13.95685 17.82717 36.98823
10.00 48.00000 44.34622 44.34622 48.00000 36.73761 39.80557 37.59266 18.17033 14.18112 17.65147 72.34853 57.72584 60.57793 88.69244 36.73761 45.00000 25.97741 45.00000 25.97741 301.59289 14.85149 17.09672 35.65655
11.00 48.00000 44.34622 44.34622 48.00000 36.73761 42.51045 40.26091 17.54124 14.98633 16.97949 73.02051 60.15868 62.90055 88.69244 36.73761 45.00000 25.97741 45.00000 25.97741 301.59289 15.63663 16.38538 34.33992
12.00 48.00000 44.34622 44.34622 48.00000 36.73761 45.00000 42.73421 16.92206 15.69986 16.32495 73.67505 62.71502 65.34973 88.69244 36.73761 45.00000 25.97741 45.00000 25.97741 301.59289 16.32495 15.69986 33.05293
13.00 48.00000 44.34622 44.34622 48.00000 36.73761 47.29061 45.02490 16.31823 16.33166 15.69286 74.30714 65.38039 67.91177 88.69244 36.73761 45.00000 25.97741 45.00000 25.97741 301.59289 16.92844 15.04434 31.80597
14.00 48.00000 44.34622 44.34622 48.00000 36.73761 49.39871 47.14593 15.73362 16.89118 15.08643 74.91357 68.14199 70.57438 88.69244 36.73761 45.00000 25.97741 45.00000 25.97741 301.59289 17.45807 14.42113 30.60601
15.00 48.00000 44.34622 44.34622 48.00000 36.73761 51.34019 49.11026 15.17078 17.38708 14.50750 75.49250 70.98859 73.32661 88.69244 36.73761 45.00000 25.97741 45.00000 25.97741 301.59289 17.92362 13.83109 29.45724
16.00 48.00000 44.34622 44.34622 48.00000 36.73761 53.13010 50.93051 14.63126 17.82717 13.95685 76.04315 73.91036 76.15875 88.69244 36.73761 45.00000 25.97741 45.00000 25.97741 301.59289 18.33369 13.27412 28.36181
17.00 48.00000 44.34622 44.34622 48.00000 36.73761 54.78241 52.61867 14.11581 18.21841 13.43450 76.56550 76.89875 79.06220 88.69244 36.73761 45.00000 25.97741 45.00000 25.97741 301.59289 18.69578 12.74939 27.32026
18.00 48.00000 44.34622 44.34622 48.00000 36.73761 56.30993 54.18598 13.62458 18.56691 12.93994 77.06006 79.94628 82.02939 88.69244 36.73761 45.00000 25.97741 45.00000 25.97741 301.59289 19.01633 12.25568 26.33203
19.00 48.00000 44.34622 44.34622 48.00000 36.73761 57.72436 55.64286 13.15727 18.87803 12.47228 77.52772 83.04644 85.05366 88.69244 36.73761 45.00000 25.97741 45.00000 25.97741 301.59289 19.30092 11.79147 25.39573
20.00 48.00000 44.34622 44.34622 48.00000 36.73761 59.03624 56.99888 12.71330 19.15643 12.03040 77.96960 86.19355 88.12912 88.69244 36.73761 45.00000 25.97741 45.00000 25.97741 301.59289 19.55429 11.35509 24.50949
21.00 48.00000 44.34622 44.34622 48.00000 36.73761 60.25512 58.26280 12.29185 19.40614 11.61303 78.38697 89.38266 91.25060 88.69244 36.73761 45.00000 25.97741 45.00000 25.97741 301.59289 19.78052 10.94486 23.67108
22.00 48.00000 44.34622 44.34622 48.00000 36.73761 61.38954 59.44258 11.89198 19.63069 11.21884 78.78116 92.60942 94.41354 88.69244 36.73761 45.00000 25.97741 45.00000 25.97741 301.59289 19.98310 10.55905 22.87807
23.00 48.00000 44.34622 44.34622 48.00000 36.73761 62.44719 60.54544 11.51267 19.83309 10.84648 79.15352 95.87003 97.61391 88.69244 36.73761 45.00000 25.97741 45.00000 25.97741 301.59289 20.16503 10.19602 22.12799
24.00 48.00000 44.34622 44.34622 48.00000 36.73761 63.43495 61.57792 11.15286 20.01600 10.49462 79.50538 99.16116 100.84814 88.69244 36.73761 45.00000 25.97741 45.00000 25.97741 301.59289 20.32886 9.85418 21.41834
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 = 67.50000
Roof Surface Angle C Bay # 0 = 45.00000
Roof Surface Angle B Bay # 0 = 67.50000

Roof Surface Angle A Bay # 1 = 67.57001
Roof Surface Angle C Bay # 1 = 44.85998
Roof Surface Angle B Bay # 1 = 67.57001

Roof Surface Angle A Bay # 2 = 67.77617
Roof Surface Angle C Bay # 2 = 44.44766
Roof Surface Angle B Bay # 2 = 67.77617

Roof Surface Angle A Bay # 3 = 68.10746
Roof Surface Angle C Bay # 3 = 43.78508
Roof Surface Angle B Bay # 3 = 68.10746

Roof Surface Angle A Bay # 4 = 68.54728
Roof Surface Angle C Bay # 4 = 42.90543
Roof Surface Angle B Bay # 4 = 68.54728

Roof Surface Angle A Bay # 5 = 69.07560
Roof Surface Angle C Bay # 5 = 41.84881
Roof Surface Angle B Bay # 5 = 69.07560

Roof Surface Angle A Bay # 6 = 69.67114
Roof Surface Angle C Bay # 6 = 40.65771
Roof Surface Angle B Bay # 6 = 69.67114

Roof Surface Angle A Bay # 7 = 70.31335
Roof Surface Angle C Bay # 7 = 39.37329
Roof Surface Angle B Bay # 7 = 70.31335

Roof Surface Angle A Bay # 8 = 70.98367
Roof Surface Angle C Bay # 8 = 38.03267
Roof Surface Angle B Bay # 8 = 70.98367

Roof Surface Angle A Bay # 9 = 71.66631
Roof Surface Angle C Bay # 9 = 36.66738
Roof Surface Angle B Bay # 9 = 71.66631

Roof Surface Angle A Bay # 10 = 72.34853
Roof Surface Angle C Bay # 10 = 35.30294
Roof Surface Angle B Bay # 10 = 72.34853

Roof Surface Angle A Bay # 11 = 73.02051
Roof Surface Angle C Bay # 11 = 33.95897
Roof Surface Angle B Bay # 11 = 73.02051

Roof Surface Angle A Bay # 12 = 73.67505
Roof Surface Angle C Bay # 12 = 32.64990
Roof Surface Angle B Bay # 12 = 73.67505

Roof Surface Angle A Bay # 13 = 74.30714
Roof Surface Angle C Bay # 13 = 31.38571
Roof Surface Angle B Bay # 13 = 74.30714

Roof Surface Angle A Bay # 14 = 74.91357
Roof Surface Angle C Bay # 14 = 30.17286
Roof Surface Angle B Bay # 14 = 74.91357

Roof Surface Angle A Bay # 15 = 75.49250
Roof Surface Angle C Bay # 15 = 29.01499
Roof Surface Angle B Bay # 15 = 75.49250

Roof Surface Angle A Bay # 16 = 76.04315
Roof Surface Angle C Bay # 16 = 27.91369
Roof Surface Angle B Bay # 16 = 76.04315

Roof Surface Angle A Bay # 17 = 76.56550
Roof Surface Angle C Bay # 17 = 26.86900
Roof Surface Angle B Bay # 17 = 76.56550

Roof Surface Angle A Bay # 18 = 77.06006
Roof Surface Angle C Bay # 18 = 25.87988
Roof Surface Angle B Bay # 18 = 77.06006

Roof Surface Angle A Bay # 19 = 77.52772
Roof Surface Angle C Bay # 19 = 24.94456
Roof Surface Angle B Bay # 19 = 77.52772

Roof Surface Angle A Bay # 20 = 77.96960
Roof Surface Angle C Bay # 20 = 24.06079
Roof Surface Angle B Bay # 20 = 77.96960

Roof Surface Angle A Bay # 21 = 78.38697
Roof Surface Angle C Bay # 21 = 23.22605
Roof Surface Angle B Bay # 21 = 78.38697

Roof Surface Angle A Bay # 22 = 78.78116
Roof Surface Angle C Bay # 22 = 22.43768
Roof Surface Angle B Bay # 22 = 78.78116

Roof Surface Angle A Bay # 23 = 79.15352
Roof Surface Angle C Bay # 23 = 21.69296
Roof Surface Angle B Bay # 23 = 79.15352

Roof Surface Angle A Bay # 24 = 79.50538
Roof Surface Angle C Bay # 24 = 20.98924
Roof Surface Angle B Bay # 24 = 79.50538