Acronym | ... |
Name | aoc3ooo3cao *b3oca&#zd |
Circumradius | sqrt[(a^{2}+ac+c^{2})/2] |
Confer |
This polychoron is isogonal only. It requires for 2 edge sizes a and d. (c here is a pseudo edge only.)
The transition a → c will result in qoq3ooo3qqo *b3oqq&#zx (rico). Then the a edges also become pseudo ones too, the incidences then would differ accordingly. Esp. the pyritohedral ikes become coes and each adjoin of a regular tet and the 4 adjoining triangular pyramids becomes a cube.
The transition a → 0 will result in ooq3ooo3qoo *b3oqo&#zx (ico). Then the regular tet degenerate into points and the triangular pyramids into edes. And the pyritohedral ikes become octs.
Incidence matrix according to Dynkin symbol
aoc3ooo3cao *b3oca&#zd → height = 0 a < c d = sqrt[(a^{2}-ac+c^{2})/2] o..3o..3o.. *b3o.. & | 96 | 3 6 | 3 9 3 | 1 4 3 -------------------------+----+---------+-----------+--------- a.. ... ... ... & | 2 | 144 * | 2 2 0 | 1 2 1 oo.3oo.3oo. *b3oo.&#d & | 2 | * 288 | 0 2 1 | 0 1 2 -------------------------+----+---------+-----------+--------- a..3o.. ... ... & | 3 | 3 0 | 96 * * | 1 1 0 ao. ... ... ...&#d & | 3 | 1 2 | * 288 * | 0 1 1 ooo3ooo3ooo *b3ooo&#d | 3 | 0 3 | * * 96 | 0 0 2 -------------------------+----+---------+-----------+--------- a..3o.. ... *b3o.. & | 4 | 6 0 | 4 0 0 | 24 * * a-tetrahedron ao.3oo. ... ...&#d & | 4 | 3 3 | 1 3 0 | * 96 * (a,d)-sized triangular pyramid aoc ... cao oca&#zd | 12 | 6 24 | 0 12 8 | * * 24 (a,d)-sized pyritohedral ike
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