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From Wolfram MathWorld. The word polyhedron has slightly different meanings in geometry and algebraic geometry.

from Wolfram MathWorld

In geometry, a polyhedron is simply a three-dimensional solid which consists of a collection of polygons, usually joined at their edges. The word derives from the Greek poly (many) plus the Indo-European hedron (seat). A polyhedron is the three-dimensional version of the more general polytope (in the geometric sense), which can be defined in arbitrary dimension. The plural of polyhedron is "polyhedra" (or sometimes "polyhedrons"). The term "polyhedron" is used somewhat differently in algebraic topology, where it is defined as a space that can be built from such "building blocks" as line segments, triangles, tetrahedra, and their higher dimensional analogs by "gluing them together" along their faces (Munkres 1993, p. 2).

Introduction. HexDome Introduction to Hexagonal Geodesic Domes Most conventional geodesic domes are based on a triangular tesselation.

Introduction

They are "high frequency" variants of an icosahedron: However, this is not how nature builds apparatus such as the eyes of flies: Also, it's not what Haekel's drawings of radiolaria showed: What is a geodesic dome and its digitizing. Voronoi. How can I map a normal triangular grid on a freeform surface...??? Standardized Surface Triangulation 1/2. Folded plane subdivided into equilateral triangles. Hello grasshoppers, I'm student of architecture and I'm new here.

Folded plane subdivided into equilateral triangles

For my current project I need a folded plane witch is subdivided into equilateral triangles, as you can see at the image attached. I've been searching through the world wide web until I arrived here and also serched for the soluton for my problem, but I haven't found the right fing, until yet. Kangaroo Mesh Machine uncomplete mesh.

Iterative Interpretations Files. Archive » Triangulate Surface Grasshopper Definition. Triangulation Scrip with EQUILATERAL TRIANGLES. Hello everyone, I need a help regarding rhino scripting.

Triangulation Scrip with EQUILATERAL TRIANGLES

I'm a 5th yr B.Arch. student from India, currently doing my thesis on " Exploring principles of plectic architecture to design a system for activating urban voids ". For the same, i'm require a RHINO SCRIPT which can probably TRIANGULATE a surface or guide a form/surface, using EQUAL SIZED EQUILATERAL TRIANGLES (of size 5m, in my case). Ive come across a lot of rhino scripts for triangulation with fabrication drawings, apart from conventional methods of triangulation in Rhinoceros, but could not tweak the script desirably. Please help! Regards Sushant Verma sushantverma16@gmail.com Tags: equal, equilateral, rhino, script, size, triangulate, triangulation.

Freeform Surfaces from Equilateral Panels. Triangular mesh with edges of equal length. Distribute points regularly on a brep. Ewha Laboratory for Innovative Architecture. Mouse : Hexagonal Frame 이번에는 Grasshopper 상에서 어떻게 Hexagonal Frame 을 만들수 있는지 보지요..

Ewha Laboratory for Innovative Architecture

Digital Architecture 수강 학생들은 수업에서 해봤을 겁니다. 물론 여기서 보는 이미지는 수업에서 한 것 보다는 약간 더 디테일하게 모듈의 scale 까지 조절이 되어 만들어 졌으니, 아래의 definition 을 참고 하세요. Bottle : Folded Surfaces Panelling 중간 시험은 잘들 보셨나요? 이 study는 3d voronoi 라는 frame 을 부드럽게 relaxation 한 구조체입니다. offline 모임에 오신분들은 보셨지요? ELIA Header Design 이번에는 분위기를 바꿔서 블로그 상단에 보이는 배꽃 header 만들기에 도전해 봅시다. 아래부터 사진 이미지/디지털화된 이미지/포토샵에서합성 / GH 코드 ; Live Components ( Tutorial for ‘1_4 Gradient Pixelization’ 참고하세요. Bottle : Re-orienting Section Planes 이번에는 Sectioning 한 parametric model 을 새로운 curve를 따라 re-orienting 해서 자유로운 sectional deformation을 만듭니다.

기본적으로 하나의 free curve를 그리시도, 간단하게 orient plane components들을 각 points와 seciton curves 에 적용하시면 됩니다. Bottle : Parametric Sectioning 자, 그러면 이제 Parametric 을 한번 해보지요. Triangulation Frame from 3D Voronoi points - Live Components Tutorial. Principal curvature lines on surfaces: need some advice please. Hi, To generate a grid structure based on a surface, I wanted to determine the principal curvature lines in a UV-point.

Principal curvature lines on surfaces: need some advice please

This seems more complex than it sounds. Though, there is a Principal curvature component in GH, and it outputs the two values for the principal curvature in that point, and the two orthogonal directions. But how to construct a curve based on that data? Anyone willing to share some experience? Using Geodesic component 1. 01_iris dome.mov. Planar Quadrilateral : Grasshopper Workshop @ Tamkang University - Flowing Bits. Scale-translation-surface This workshop is invited by professor Chen-Cheng Chen from the architecture department of Tamkang University.

Planar Quadrilateral : Grasshopper Workshop @ Tamkang University - Flowing Bits

It focuses on the particular geometry of planar quadrilateral(PQ) mesh. PQ mesh draws interests from architects in recent years because of its constructability. There are many advantages using PQ over triangulation when discretizing a freeform surface. For more information on PQ mesh and descretization, see paper A parametric strategy for free-form glass structures using quadrilateral planar facets by Glymph at el. and Discrete Surfaces for Architectural Design by Pottmann et al.

PQ strip The paper by Glymph at el. introduces several methods to construct a PQ mesh. Planar Quad Unroll PQ grasshopper definition There are two things worth noting in the definition. If the model is going to be fabricated with planar material, tabs might need to be added to the faces for construction. Download the definition file here. SmartForm - SMART Solutions Network. SmartForm is a component that is used for applying dynamic relaxation on a SmartMesh.

SmartForm - SMART Solutions Network

A SmartMesh can be created from a mesh or a list of lines. SmartForm should be considered as a conceptual tool for modeling structural efficient forms. Since it is a conceptual tool input and outputs should not be considered as exact values, by exact values meaning for instance exact forces, stiffness. Schwarz P - Gyroid - Diamond - Neovius - iWP - PH Hybrid. Populate by gradient RGB. Is there anybody have examples for image sampler !

Voronoi + honeycomb. Easily Create Graphical User Interfaces in Rhino Python. I have been doing some work for the Taubman College of Architecture Fabrication Lab.

Easily Create Graphical User Interfaces in Rhino Python

I've been working on some Graphical User Interface helper classes for use in Rhino Python. The idea behind these classes is they allow you to create custom, floating dialog user interfaces without having to use a UI creation tool like SharpDevelop. I thought these would be generally useful so I made them free to download and use. Use the link below to download a ZIP file of everything you'll need. Download the Code Getting Started Simply unzip the file into a directory of your choice. Here are a few examples of UIs you can easily make. Circle UI Example.py This is the most basic example. Relative Prime UI Example.py. Aether – simple speedy spatial fields for Grasshopper. Spatially varying fields, which associate a value (such as a number or a vector) to every point in space, have a wide range of applications.

Aether – simple speedy spatial fields for Grasshopper

I wanted a simple way of defining such a field in a Grasshopper script component as an equation, or a function of distance to some geometry, then passing this field to another script component, in a way that the downstream component can easily query the value of the field at any point. For speed reasons I did not want to do this by passing millions of sample values. Various tools for fields do already exist in Grasshopper, both natively and as plugins, but of the ones I looked at, I couldn't find any that provided the flexibility and speed I wanted, so I put together a very simple library. For now this includes scalar, vector and frame fields. With the scalar fields, I also made an implicit surface tool.

Here I've come up with a different approach, consisting of two stages. The first part of this is a voxelized threshold of the field. Venation 2D. [ EasyToDo Venation ] Stochastic Fractal Definition. With anenome 0.2 now released, here's a sample for how to use the multiple data input/outputs via a play with fractals. You'll also need weaverbird. Tags: anenome, weaverbird Attachments: 131221_anenome_fractal_tree.gh, 35 KB ▶ Reply to This. Rhinoceros 5. Flattening surface. Rhino Polyhedra. Voronoi Structure. Voronoi vase. Kinetic Ceiling Parametric Design. Parametric Truss Part 1. Loft Waffle Grasshopper Tutorial *full* Creating a 3d Waffle Model in Rhino - Part 1. Grasshopper - 3D voronoi_1 part. 3/3. Grasshopper - Turtle Skin(1)