Developmental Geometry for a Pyramid with an (7 sided) Polygonal Base
Polygonal Trigonometric Functions are to 5 Decimal Places


central angle = 51.4285714285714
working angle = 25.7142857142857
plan angle = 64.2857142857143
miter angle = 5.78 & 12
hip run per foot = 13.3189951700969
apothem multiplier = secant(360 ( N 2 ))
side wall multiplier = tan((360 (N 2 )) 2
apothem_multiplier = 1.10991626417474
side_wall_multiplier = 0.963149237615057
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 43.24651 43.24651 48.00000 41.65284 0.00000 0.00000 25.71429 0.00000 25.71429 64.28571 43.24651 48.00000 86.49301 41.65284 51.42857 25.97012 38.57143 32.56550 301.59289 0.00000 25.71429 51.42857
1.00 48.00000 43.24651 43.24651 48.00000 41.65284 4.76364 4.29375 25.65139 2.06493 25.63687 64.36313 43.39641 48.13510 86.49301 41.65284 51.42857 25.97012 38.57143 32.56550 301.59289 2.29019 25.61901 51.28423
2.00 48.00000 43.24651 43.24651 48.00000 41.65284 9.46232 8.53981 25.46544 4.09038 25.40876 64.59124 43.84304 48.53815 86.49301 41.65284 51.42857 25.97012 38.57143 32.56550 301.59289 4.52669 25.33945 50.85838
3.00 48.00000 43.24651 43.24651 48.00000 41.65284 14.03624 12.69359 25.16435 6.04055 25.04179 64.95821 44.57748 49.20255 86.49301 41.65284 51.42857 25.97012 38.57143 32.56550 301.59289 6.66191 24.89326 50.17161
4.00 48.00000 43.24651 43.24651 48.00000 41.65284 18.43495 16.71622 24.76028 7.88621 24.55385 65.44615 45.58582 50.11793 86.49301 41.65284 51.42857 25.97012 38.57143 32.56550 301.59289 8.65889 24.30653 49.25526
5.00 48.00000 43.24651 43.24651 48.00000 41.65284 22.61986 20.57632 24.26835 9.60637 23.96660 66.03340 46.85038 51.27083 86.49301 41.65284 51.42857 25.97012 38.57143 32.56550 301.59289 10.49346 23.60994 48.14768
6.00 48.00000 43.24651 43.24651 48.00000 41.65284 26.56505 24.25082 23.70525 11.18857 23.30316 66.69684 48.35106 52.64566 86.49301 41.65284 51.42857 25.97012 38.57143 32.56550 301.59289 12.15396 22.83492 46.89032
7.00 48.00000 43.24651 43.24651 48.00000 41.65284 30.25644 27.72485 23.08787 12.62808 22.58604 67.41396 50.06664 54.22553 86.49301 41.65284 51.42857 25.97012 38.57143 32.56550 301.59289 13.63929 22.01069 45.52416
8.00 48.00000 43.24651 43.24651 48.00000 41.65284 33.69007 30.99096 22.43226 13.92641 21.83569 68.16431 51.97583 55.99310 86.49301 41.65284 51.42857 25.97012 38.57143 32.56550 301.59289 14.95617 21.16243 44.08707
9.00 48.00000 43.24651 43.24651 48.00000 41.65284 36.86990 34.04794 21.75289 15.08966 21.06966 68.93034 54.05813 57.93118 86.49301 41.65284 51.42857 25.97012 38.57143 32.56550 301.59289 16.11637 20.31047 42.61214
10.00 48.00000 43.24651 43.24651 48.00000 41.65284 39.80557 36.89949 21.06221 16.12689 20.30225 69.69775 56.29433 60.02326 86.49301 41.65284 51.42857 25.97012 38.57143 32.56550 301.59289 17.13435 19.47033 41.12691
11.00 48.00000 43.24651 43.24651 48.00000 41.65284 42.51045 39.55290 20.37056 17.04879 19.54459 70.45541 58.66684 62.25382 86.49301 41.65284 51.42857 25.97012 38.57143 32.56550 301.59289 18.02550 18.65320 39.65333
12.00 48.00000 43.24651 43.24651 48.00000 41.65284 45.00000 42.01787 19.68615 17.86662 18.80498 71.19502 61.15979 64.60852 86.49301 41.65284 51.42857 25.97012 38.57143 32.56550 301.59289 18.80498 17.86662 38.20814
13.00 48.00000 43.24651 43.24651 48.00000 41.65284 47.29061 44.30559 19.01532 18.59153 18.08924 71.91076 63.75907 67.07427 86.49301 41.65284 51.42857 25.97012 38.57143 32.56550 301.59289 19.48697 17.11525 36.80355
14.00 48.00000 43.24651 43.24651 48.00000 41.65284 49.39871 46.42797 18.36271 19.23413 17.40123 72.59877 66.45218 69.63930 86.49301 41.65284 51.42857 25.97012 38.57143 32.56550 301.59289 20.08437 16.40157 35.44796
15.00 48.00000 43.24651 43.24651 48.00000 41.65284 51.34019 48.39707 17.73160 19.80416 16.74325 73.25675 69.22819 72.29303 86.49301 41.65284 51.42857 25.97012 38.57143 32.56550 301.59289 20.60860 15.72646 34.14674
16.00 48.00000 43.24651 43.24651 48.00000 41.65284 53.13010 50.22474 17.12411 20.31047 16.11637 73.88363 72.07751 75.02604 86.49301 41.65284 51.42857 25.97012 38.57143 32.56550 301.59289 21.06966 15.08966 32.90286
17.00 48.00000 43.24651 43.24651 48.00000 41.65284 54.78241 51.92235 16.54147 20.76091 15.52082 74.47918 74.99179 77.83000 86.49301 41.65284 51.42857 25.97012 38.57143 32.56550 301.59289 21.47621 14.49014 31.71748
18.00 48.00000 43.24651 43.24651 48.00000 41.65284 56.30993 53.50063 15.98422 21.16243 14.95617 75.04383 77.96375 80.69749 86.49301 41.65284 51.42857 25.97012 38.57143 32.56550 301.59289 21.83569 13.92641 30.59043
19.00 48.00000 43.24651 43.24651 48.00000 41.65284 57.72436 54.96955 15.45237 21.52110 14.42156 75.57844 80.98703 83.62200 86.49301 41.65284 51.42857 25.97012 38.57143 32.56550 301.59289 22.15448 13.39664 29.52060
20.00 48.00000 43.24651 43.24651 48.00000 41.65284 59.03624 56.33838 14.94553 21.84224 13.91582 76.08418 84.05610 86.59773 86.49301 41.65284 51.42857 25.97012 38.57143 32.56550 301.59289 22.43802 12.89890 28.50619
21.00 48.00000 43.24651 43.24651 48.00000 41.65284 60.25512 57.61558 14.46307 22.13045 13.43764 76.56236 87.16612 89.61960 86.49301 41.65284 51.42857 25.97012 38.57143 32.56550 301.59289 22.69097 12.43117 27.54500
22.00 48.00000 43.24651 43.24651 48.00000 41.65284 61.38954 58.80892 14.00413 22.38973 12.98558 77.01442 90.31286 92.68308 86.49301 41.65284 51.42857 25.97012 38.57143 32.56550 301.59289 22.91729 11.99148 26.63454
23.00 48.00000 43.24651 43.24651 48.00000 41.65284 62.44719 59.92544 13.56776 22.62355 12.55817 77.44183 93.49262 95.78418 86.49301 41.65284 51.42857 25.97012 38.57143 32.56550 301.59289 23.12039 11.57789 25.77223
24.00 48.00000 43.24651 43.24651 48.00000 41.65284 63.43495 60.97156 13.15292 22.83492 12.15396 77.84604 96.70213 98.91937 86.49301 41.65284 51.42857 25.97012 38.57143 32.56550 301.59289 23.30316 11.18857 24.95539
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 = 64.28571
Roof Surface Angle C Bay # 0 = 51.42857
Roof Surface Angle B Bay # 0 = 64.28571

Roof Surface Angle A Bay # 1 = 64.36313
Roof Surface Angle C Bay # 1 = 51.27374
Roof Surface Angle B Bay # 1 = 64.36313

Roof Surface Angle A Bay # 2 = 64.59124
Roof Surface Angle C Bay # 2 = 50.81752
Roof Surface Angle B Bay # 2 = 64.59124

Roof Surface Angle A Bay # 3 = 64.95821
Roof Surface Angle C Bay # 3 = 50.08359
Roof Surface Angle B Bay # 3 = 64.95821

Roof Surface Angle A Bay # 4 = 65.44615
Roof Surface Angle C Bay # 4 = 49.10770
Roof Surface Angle B Bay # 4 = 65.44615

Roof Surface Angle A Bay # 5 = 66.03340
Roof Surface Angle C Bay # 5 = 47.93320
Roof Surface Angle B Bay # 5 = 66.03340

Roof Surface Angle A Bay # 6 = 66.69684
Roof Surface Angle C Bay # 6 = 46.60632
Roof Surface Angle B Bay # 6 = 66.69684

Roof Surface Angle A Bay # 7 = 67.41396
Roof Surface Angle C Bay # 7 = 45.17208
Roof Surface Angle B Bay # 7 = 67.41396

Roof Surface Angle A Bay # 8 = 68.16431
Roof Surface Angle C Bay # 8 = 43.67139
Roof Surface Angle B Bay # 8 = 68.16431

Roof Surface Angle A Bay # 9 = 68.93034
Roof Surface Angle C Bay # 9 = 42.13933
Roof Surface Angle B Bay # 9 = 68.93034

Roof Surface Angle A Bay # 10 = 69.69775
Roof Surface Angle C Bay # 10 = 40.60450
Roof Surface Angle B Bay # 10 = 69.69775

Roof Surface Angle A Bay # 11 = 70.45541
Roof Surface Angle C Bay # 11 = 39.08919
Roof Surface Angle B Bay # 11 = 70.45541

Roof Surface Angle A Bay # 12 = 71.19502
Roof Surface Angle C Bay # 12 = 37.60995
Roof Surface Angle B Bay # 12 = 71.19502

Roof Surface Angle A Bay # 13 = 71.91076
Roof Surface Angle C Bay # 13 = 36.17847
Roof Surface Angle B Bay # 13 = 71.91076

Roof Surface Angle A Bay # 14 = 72.59877
Roof Surface Angle C Bay # 14 = 34.80246
Roof Surface Angle B Bay # 14 = 72.59877

Roof Surface Angle A Bay # 15 = 73.25675
Roof Surface Angle C Bay # 15 = 33.48649
Roof Surface Angle B Bay # 15 = 73.25675

Roof Surface Angle A Bay # 16 = 73.88363
Roof Surface Angle C Bay # 16 = 32.23275
Roof Surface Angle B Bay # 16 = 73.88363

Roof Surface Angle A Bay # 17 = 74.47918
Roof Surface Angle C Bay # 17 = 31.04165
Roof Surface Angle B Bay # 17 = 74.47918

Roof Surface Angle A Bay # 18 = 75.04383
Roof Surface Angle C Bay # 18 = 29.91235
Roof Surface Angle B Bay # 18 = 75.04383

Roof Surface Angle A Bay # 19 = 75.57844
Roof Surface Angle C Bay # 19 = 28.84312
Roof Surface Angle B Bay # 19 = 75.57844

Roof Surface Angle A Bay # 20 = 76.08418
Roof Surface Angle C Bay # 20 = 27.83165
Roof Surface Angle B Bay # 20 = 76.08418

Roof Surface Angle A Bay # 21 = 76.56236
Roof Surface Angle C Bay # 21 = 26.87528
Roof Surface Angle B Bay # 21 = 76.56236

Roof Surface Angle A Bay # 22 = 77.01442
Roof Surface Angle C Bay # 22 = 25.97115
Roof Surface Angle B Bay # 22 = 77.01442

Roof Surface Angle A Bay # 23 = 77.44183
Roof Surface Angle C Bay # 23 = 25.11634
Roof Surface Angle B Bay # 23 = 77.44183

Roof Surface Angle A Bay # 24 = 77.84604
Roof Surface Angle C Bay # 24 = 24.30792
Roof Surface Angle B Bay # 24 = 77.84604