Mesh of Leonardo da Vinci's 72-sided sphere (Campanus' sphere, septuaginta)

septuaginta.off

OFF
62 72 0

0.866025403784439 0.5 0
0.5 0.866025403784439 0
0 1 0
-0.5 0.866025403784439 0
-0.866025403784439 0.5 0
-1 0 0
-0.866025403784439 -0.5 0
-0.5 -0.866025403784438 0
0 -1 0
0.5 -0.866025403784439 0
0.866025403784438 -0.5 0
1 0 0
0.75 0.5 -0.433012701892219
0.433012701892219 0.866025403784439 -0.25
-0.433012701892219 0.866025403784439 0.25
-0.75 0.5 0.433012701892219
-0.866025403784439 0 0.5
-0.75 -0.5 0.433012701892219
-0.43301270189222 -0.866025403784438 0.25
0.433012701892219 -0.866025403784439 -0.25
0.75 -0.5 -0.433012701892219
0.866025403784439 0 -0.5
0.43301270189222 0.5 -0.75
0.25 0.866025403784439 -0.433012701892219
-0.25 0.866025403784439 0.433012701892219
-0.43301270189222 0.5 0.75
-0.5 0 0.866025403784439
-0.43301270189222 -0.5 0.75
-0.25 -0.866025403784438 0.43301270189222
0.25 -0.866025403784439 -0.433012701892219
0.433012701892219 -0.5 -0.75
0.5 0 -0.866025403784439
0 0.5 -0.866025403784439
0 0.866025403784439 -0.5
0 0.866025403784439 0.5
0 0.5 0.866025403784439
0 0 1
0 -0.5 0.866025403784439
0 -0.866025403784438 0.5
0 -0.866025403784439 -0.5
0 -0.5 -0.866025403784438
0 0 -1
-0.433012701892219 0.5 -0.75
-0.25 0.866025403784439 -0.43301270189222
0.25 0.866025403784439 0.433012701892219
0.433012701892219 0.5 0.75
0.5 0 0.866025403784439
0.433012701892219 -0.5 0.75
0.25 -0.866025403784438 0.43301270189222
-0.25 -0.866025403784439 -0.43301270189222
-0.433012701892219 -0.5 -0.75
-0.5 0 -0.866025403784439
-0.75 0.5 -0.43301270189222
-0.433012701892219 0.866025403784439 -0.25
0.433012701892219 0.866025403784439 0.25
0.75 0.5 0.43301270189222
0.866025403784438 0 0.5
0.75 -0.5 0.43301270189222
0.43301270189222 -0.866025403784438 0.25
-0.433012701892219 -0.866025403784439 -0.25
-0.75 -0.5 -0.433012701892219
-0.866025403784438 0 -0.5
4  4 5 16 15
4  52 61 5 4
4  55 56 11 0
4  0 11 21 12
4  42 51 61 52
4  15 16 26 25
4  25 26 36 35
4  36 37 47 46
4  45 46 56 55
4  35 36 46 45
3  2 43 53
4  52 53 43 42
4  46 47 57 56
4  10 11 56 57
3  2 13 23
3  2 24 34
3  34 44 2
4  24 25 35 34
4  34 35 45 44
3  1 13 2
4  12 13 1 0
3  2 53 3
4  53 52 4 3
4  20 21 11 10
4  30 31 21 20
3  9 58 8
4  9 10 57 58
3  33 43 2
3  2 23 33
4  12 21 31 22
4  22 23 13 12
3  2 44 54
3  54 1 2
4  44 45 55 54
4  0 1 54 55
3  18 7 8
3  8 28 18
3  38 28 8
4  26 27 37 36
4  27 28 38 37
3  14 24 2
3  2 3 14
4  14 15 25 24
4  3 4 15 14
4  40 41 31 30
4  50 51 41 40
4  61 60 6 5
4  60 61 51 50
3  19 9 8
4  19 20 10 9
4  32 41 51 42
4  22 31 41 32
4  42 43 33 32
4  32 33 23 22
3  8 58 48
3  48 38 8
4  47 48 58 57
4  37 38 48 47
4  5 6 17 16
4  16 17 27 26
4  6 7 18 17
4  17 18 28 27
3  8 7 59
3  59 49 8
4  60 59 7 6
4  59 60 50 49
3  8 49 39
4  49 50 40 39
3  29 19 8
3  8 39 29
4  29 30 20 19
4  39 40 30 29

septuaginta.R

library(rgl)

septuaginta <- mesh3d(
  rbind(
    c(0.866025403784439, 0.5, 0),
    c(0.5, 0.866025403784439, 0),
    c(0, 1, 0),
    c(-0.5, 0.866025403784439, 0),
    c(-0.866025403784439, 0.5, 0),
    c(-1, 0, 0),
    c(-0.866025403784439, -0.5, 0),
    c(-0.5, -0.866025403784438, 0),
    c(0, -1, 0),
    c(0.5, -0.866025403784439, 0),
    c(0.866025403784438, -0.5, 0),
    c(1, 0, 0),
    c(0.75, 0.5, -0.433012701892219),
    c(0.433012701892219, 0.866025403784439, -0.25),
    c(-0.433012701892219, 0.866025403784439, 0.25),
    c(-0.75, 0.5, 0.433012701892219),
    c(-0.866025403784439, 0, 0.5),
    c(-0.75, -0.5, 0.433012701892219),
    c(-0.43301270189222, -0.866025403784438, 0.25),
    c(0.433012701892219, -0.866025403784439, -0.25),
    c(0.75, -0.5, -0.433012701892219),
    c(0.866025403784439, 0, -0.5),
    c(0.43301270189222, 0.5, -0.75),
    c(0.25, 0.866025403784439, -0.433012701892219),
    c(-0.25, 0.866025403784439, 0.433012701892219),
    c(-0.43301270189222, 0.5, 0.75),
    c(-0.5, 0, 0.866025403784439),
    c(-0.43301270189222, -0.5, 0.75),
    c(-0.25, -0.866025403784438, 0.43301270189222),
    c(0.25, -0.866025403784439, -0.433012701892219),
    c(0.433012701892219, -0.5, -0.75),
    c(0.5, 0, -0.866025403784439),
    c(0, 0.5, -0.866025403784439),
    c(0, 0.866025403784439, -0.5),
    c(0, 0.866025403784439, 0.5),
    c(0, 0.5, 0.866025403784439),
    c(0, 0, 1),
    c(0, -0.5, 0.866025403784439),
    c(0, -0.866025403784438, 0.5),
    c(0, -0.866025403784439, -0.5),
    c(0, -0.5, -0.866025403784438),
    c(0, 0, -1),
    c(-0.433012701892219, 0.5, -0.75),
    c(-0.25, 0.866025403784439, -0.43301270189222),
    c(0.25, 0.866025403784439, 0.433012701892219),
    c(0.433012701892219, 0.5, 0.75),
    c(0.5, 0, 0.866025403784439),
    c(0.433012701892219, -0.5, 0.75),
    c(0.25, -0.866025403784438, 0.43301270189222),
    c(-0.25, -0.866025403784439, -0.43301270189222),
    c(-0.433012701892219, -0.5, -0.75),
    c(-0.5, 0, -0.866025403784439),
    c(-0.75, 0.5, -0.43301270189222),
    c(-0.433012701892219, 0.866025403784439, -0.25),
    c(0.433012701892219, 0.866025403784439, 0.25),
    c(0.75, 0.5, 0.43301270189222),
    c(0.866025403784438, 0, 0.5),
    c(0.75, -0.5, 0.43301270189222),
    c(0.43301270189222, -0.866025403784438, 0.25),
    c(-0.433012701892219, -0.866025403784439, -0.25),
    c(-0.75, -0.5, -0.433012701892219),
    c(-0.866025403784438, 0, -0.5)
  ),
  triangles = cbind(
    c(2, 43, 53),
    c(2, 13, 23),
    c(2, 24, 34),
    c(34, 44, 2),
    c(1, 13, 2),
    c(2, 53, 3),
    c(9, 58, 8),
    c(33, 43, 2),
    c(2, 23, 33),
    c(2, 44, 54),
    c(54, 1, 2),
    c(18, 7, 8),
    c(8, 28, 18),
    c(38, 28, 8),
    c(14, 24, 2),
    c(2, 3, 14),
    c(19, 9, 8),
    c(8, 58, 48),
    c(48, 38, 8),
    c(8, 7, 59),
    c(59, 49, 8),
    c(8, 49, 39),
    c(29, 19, 8),
    c(8, 39, 29)
  ) + 1,
  quads = cbind(
    c(4, 5, 16, 15),
    c(52, 61, 5, 4),
    c(55, 56, 11, 0),
    c(0, 11, 21, 12),
    c(42, 51, 61, 52),
    c(15, 16, 26, 25),
    c(25, 26, 36, 35),
    c(36, 37, 47, 46),
    c(45, 46, 56, 55),
    c(35, 36, 46, 45),
    c(52, 53, 43, 42),
    c(46, 47, 57, 56),
    c(10, 11, 56, 57),
    c(24, 25, 35, 34),
    c(34, 35, 45, 44),
    c(12, 13, 1, 0),
    c(53, 52, 4, 3),
    c(20, 21, 11, 10),
    c(30, 31, 21, 20),
    c(9, 10, 57, 58),
    c(12, 21, 31, 22),
    c(22, 23, 13, 12),
    c(44, 45, 55, 54),
    c(0, 1, 54, 55),
    c(26, 27, 37, 36),
    c(27, 28, 38, 37),
    c(14, 15, 25, 24),
    c(3, 4, 15, 14),
    c(40, 41, 31, 30),
    c(50, 51, 41, 40),
    c(61, 60, 6, 5),
    c(60, 61, 51, 50),
    c(19, 20, 10, 9),
    c(32, 41, 51, 42),
    c(22, 31, 41, 32),
    c(42, 43, 33, 32),
    c(32, 33, 23, 22),
    c(47, 48, 58, 57),
    c(37, 38, 48, 47),
    c(5, 6, 17, 16),
    c(16, 17, 27, 26),
    c(6, 7, 18, 17),
    c(17, 18, 28, 27),
    c(60, 59, 7, 6),
    c(59, 60, 50, 49),
    c(49, 50, 40, 39),
    c(29, 30, 20, 19),
    c(39, 40, 30, 29)
  ) + 1
)