Acronym ogpy, 8/3-pyr
Name octagrammic pyramid
Circumradius 1/sqrt[sqrt(8)] = 0.594604
Vertex figures [38/3], [3,3,8/3]
Coordinates
  • (0, 0; 1/sqrt[sqrt(8)])
  • (1/2, (sqrt(2)-1)/2; 1/sqrt[sqrt(8)]-1/sqrt[sqrt(2)])   & all permutations and all changes of sign within first 2 coords
Colonel of regiment (is itself locally convex)
Dihedral angles
  • between {3} and {8/3}:   arccos[(2-sqrt(2))/3] = 78.739962°
  • between {3} and {3}:   arccos[(sqrt(2)-1)/3] = 52.448397°
Face vector 9, 16, 9
Confer
general pyramids:
n/d-py  

Incidence matrix according to Dynkin symbol

ox8/3oo&#x   → height = 1/sqrt[sqrt(2)] = 0.840896
(pt || {8/3})

tip  o.   o.    | 1 * | 8 0 | 8 0
base .o   .o    | * 8 | 1 2 | 2 1
----------------+-----+-----+----
lace oo8/3oo&#x | 1 1 | 8 * | 2 0
base .x   ..    | 0 2 | * 8 | 1 1
----------------+-----+-----+----
coat ox   ..&#x | 1 2 | 2 1 | 8 *
base .x8/3.o    | 0 8 | 0 8 | * 1


ox4/3ox&#x   → height = 1/sqrt[sqrt(2)] = 0.840896
(pt || {8/3})

o.4/3o.    | 1 * | 8 0 0 | 8 0 0
.o4/3.o    | * 8 | 1 1 1 | 1 1 1
-----------+-----+-------+------
oo4/3oo&#x | 1 1 | 8 * * | 2 0 0
.x   ..    | 0 2 | * 4 * | 1 0 1
..   .x    | 0 2 | * * 4 | 0 1 1
-----------+-----+-------+------
ox   ..&#x | 1 2 | 2 1 0 | 4 * *
..   ox&#x | 1 2 | 2 0 1 | * 4 *
.x4/3.x    | 0 8 | 0 4 4 | * * 1

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