Acronym degpy, 10/3-pyr
Name decagrammic pyramid
Circumradius sqrt[(1+sqrt(5))/8] = 0.636010
Vertex figures [310/3], [3,3,10/3]
Colonel of regiment (is itself locally convex)
Dihedral angles
  • between {3} and {3}:   arccos[(sqrt(5)-2)/3] = 85.486768°
  • between {3} and {10/3}:   arccos[(5-sqrt(5))/6] = 62.570597°
Face vector 11, 20, 11
Confer
general pyramids:
n/d-py  

Incidence matrix according to Dynkin symbol

ox10/3oo&#x   → height = sqrt[(sqrt(5)-1)/2] = 0.786151
(pt || {10/3})

tip  o.    o.    | 1  * | 10  0 | 10 0
base .o    .o    | * 10 |  1  2 |  2 1
-----------------+------+-------+-----
lace oo10/3oo&#x | 1  1 | 10  * |  2 0
base .x    ..    | 0  2 |  * 10 |  1 1
-----------------+------+-------+-----
coat ox    ..&#x | 1  2 |  2  1 | 10 *
base .x10/3.o    | 0 10 |  0 10 | * 1


ox5/3ox&#x   → height = sqrt[(sqrt(5)-1)/2] = 0.786151
(pt || {10/3})

o.5/3o.    | 1  * | 10 0 0 | 10 0 0
.o5/3.o    | * 10 |  1 1 1 |  1 1 1
-----------+------+--------+-------
oo5/3oo&#x | 1  1 | 10 * * |  2 0 0
.x   ..    | 0  2 |  * 5 * |  1 0 1
..   .x    | 0  2 |  * * 5 |  0 1 1
-----------+------+--------+------
ox   ..&#x | 1  2 |  2 1 0 |  5 * *
..   ox&#x | 1  2 |  2 0 1 |  * 5 *
.x5/3.x    | 0 10 |  0 5 5 |  * * 1

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